RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1E.

Other Exercises

Question 1.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q1.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q1.2

Question 2.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q2.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q2.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q2.3

Question 3.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.4

Question 4.
Solution:
Product of two numbers = – 9
one number = – 12
Let second number = x
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q4.1

Question 5.
Solution:
Product of two rational numbers = \(\\ \frac { -16}{ 9 } \)
One number = \(\\ \frac { -4 }{ 3 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q5.1

Question 6.
Solution:
Let x be multiplied
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q6.1

Question 7.
Solution:
Let x be multiplied
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q7.1

Question 8.
Solution:
Let required number = x
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q8.1

Question 9.
Solution:
sum of \(\\ \frac { 13 }{ 5 } \) and \(\\ \frac { -12 }{ 7 } \)
= \(\\ \frac { 13 }{ 5 } \) + \(\\ \frac { -12 }{ 7 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q9.1

Question 10.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q10.1

Question 11.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q11.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q11.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q11.3

Question 12.
Solution:
(i) No, not always closed under division.
(ii) No, not always commutative.
(iii) No, not always associative.
(iv) No. It is not possible to divide any number by zero.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1E are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E

RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 3 Squares and Square Roots Ex 3E.

Other Exercises

Evaluate:

Question 1.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q1.1

Question 2.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q2.1

Question 3.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q3.1

Question 4.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q4.1

Question 5.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q5.1

Question 6.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q6.1

Question 7.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q7.1

Question 8.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q8.1

Question 9.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q9.1

Question 10.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q10.1

Question 11.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q11.1

Question 12.
Solution:
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q12.1

Question 13.
Solution:
Finding the square root of 2509 by division we find that 9 is left as remainder
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q13.1
9 must be subtracted to get the perfect square 100.
Least number to be subtracted = 9

Question 14.
Solution:
Finding the square root of 7581 by division method, we find that 12 is left as remainder.
12 must be subtracted from 7581 to get a perfect square i.e., 7581 – 12 = 7569
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q14.1
(i) The least number to be subtracted = 12
(ii) Perfect square = 7569
(iii) and square root = 87 Ans.

Question 15.
Solution:
Finding the square root of 6203 by division method, we find that 38 is to be added to get a perfect square.
(i) Least number to be added = 38
(ii) Perfect square = 6241
(iii) Square root = 79 Ans.
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q15.1

Question 16.
Solution:
Finding the square root of 8400 by long division method, we find that 64 is to be added to 8400,
We, get 8400 + 64 = 8464
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q16.1
Least number to be added = 64
Perfect square = 8464
Square root = 92 Ans.

Question 17.
Solution:
Least four-digit number = 1000
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q17.1
Finding the square root of 1000 by the division method, we find that 24 must be added to get a perfect square of 4 digits.
Perfect square = 1000 + 24 = 1024 Ans.
square root of 1024 = 32
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q17.2

Question 18.
Solution:
Greatest number of five digits = 99999
Finding the square root of 99999
We get remainder = 143
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q18.1
Required perfect square = 99999 – 143 = 99856
and square root = 316 Ans

Question 19.
Solution:
Area of a square field = 60025 m²
Let its side = a
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3E Q19.1

Hope given RS Aggarwal Solutions Class 8 Chapter 3 Squares and Square Roots Ex 3E are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3B

RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 3 Squares and Square Roots Ex 3B.

Other Exercises

Question 1.
Solution:
We know that a number ending in 2, 3, 7 or 8 is never a perfect square. So, (i) 5372, (ii) 5963, (iii) 8457, (iv) 9468 cannot be perfect square
Again number ending in an odd number of zeros is also never a perfect square.
Among (v) 360, (vi) 64000, (vii) 2500000 each one has odd zeros at its end. So, there cannot be a perfect square.

Question 2.
Solution:
We know that the square of an even number is also an even number.
(i) 196 (iii) 900, (v) 324 are the squares of even numbers.

Question 3.
Solution:
We know that square.of an odd number is alway is an odd number and square of an even number is always an even number.
Therefore the (ii) 961, (iv) 8649 (v) 4225 are squares of odd numbers.

Question 4.
Solution:
We know that sum of the first n odd natural numbers = n² Therefore.
(i) ∵ It ends with 13
and 1 + 3 + 5 + 7 + 9 + 11 + 13 is the sum of first 7 odd numbers
∵Its sum = (7)² = 49
(ii) 1 + 3 + 5 + 7 + 9+ 11 + 13 + 15 + 17 + 19
Here, n = 10
∵Sum = n² = (10)² = 100
(iii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)
Here, n = 12
Sum = n² = (12)² = 144 Ans.

Question 5.
Solution:
(i) 81 = (9)² = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 (Sum of first 9 odd numbers)
(ii) 100 = (10)² =1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 (Sum of first 10 odd numbers)

Question 6.
Solution:
We know that 2m, m² – 1 and m² + 1 is a Pythagorean triplet where m > 1
(i) One number = 6
∵ 2m = 6 => m = 3
∵ Other members of triplet will be
m² – 1 = (3)² – 1 = 9 – 1 = 8
and m² + 1 = (3)² + 1 = 9 + 1 = 10
∵ Pythagorean triplet is 6, 8, 10
(ii) Let 2m = 14 = m = \(\\ \frac { 14 }{ 2 } \) = 7
m² – 1 = (7)² – 1 = 49 – 1 = 48
and m² + 1 = (7)² + 1 = 49 + 1 = 50
∵Pythagorean triplet = 14, 48, 50
(iii) Let 2m = 16 => m = 8
m² – 1 = (8)² – 1 = 64 – 1 = 63
and m² + 1 = (8)² + 1 = 64 + 1 = 65
∵Pythagorean triplet =16, 63, 65
(iv) Let 2m = 20 => m = 10
∵m² – 1 = (10)² – 1 = 100 – 1 = 99
and m² + 1 = (10)² + 1 = 100 + 1 = 101
∵Pythagorean triplet = 20, 99, 101 Ans.

Question 7.
Solution:
We know that :
(n + 1)² – n² = {(n + 1) + n}
Therefore :
(i) (38)² – (37)² = 38 + 37 = 75
(ii) (75)² – (74)² = 75 + 74 = 149
(iii) (92)² – (91)² = 92 + 91 = 183
(iv) (105)² – (104)² = 105 + 104 = 209
(v) (141)² – (140)² = 141 + 140 = 281
(vi) (218)² – (217)² = 218 + 217 = 435

Question 8.
Solution:
We know that (a + b)² = a² + 2ab + b²
(i) (310)² = (300 + 10)²
= (300)² + 2 x 300 x 10 + (10)²
= 90000 + 6000 + 100 = 96100
(ii) (508)² = (500 + 8)²
= (500)² + 2 x 500 x 8 + (8)²
= 250000 + 8000 + 64 = 258064
(iii) (630)² = (600 + 30)²
= (600)² + 2 x 600 x 30 + (30)²
= 360000 + 36000 + 900 = 396900

Question 9.
Solution:
We know that (a – b)² = a² – 2ab + b²
(i) (196)² = (200 – 4)²
= (200)² – 2 x 200 x 4 + (4)²
= 40000 – 1600 + 16
= 40016 – 1600 = 38416
(ii) (689)² = (700 – 11)²
= (700)² – 2 x 700 x 11 +(11)²
= 490000 – 15400 + 121
= 490121 – 15400 = 474721
(iii) (891)² = (900 – 9)²
= (900)² – 2 x 900 x 9 + (9)²
= 810000 – 16200 + 81
= 810081 – 16200 = 793881

Question 10.
Solution:
Using (a – b) (a + b) = a² – b²
(i) 69 x 71 = (70 – 1) (70 + 1)
= (70)² – (1)² = 4900 – 1
= 4899
(ii) 94 x 106 = (100 – 6) (100 + 6)
= (100)² – (6)²
= 10000 – 36 = 9964

Question 11.
Solution:
Using (a – b) (a + b) – a² – b²
(i) 88 x 92 = (90 – 2) (90 + 2)
= (90)² – (2)²
= 8100 – 4 = 8096
(ii) 78 x 82 = (80 – 2) (80 + 2)
= (80)² – (2)²
= 6400 – 4 = 6396

Question 12.
Solution:
(i) The square of an even number is even
(ii) The square of an odd number is odd
(iii) The square of a proper fraction is less than the given fraction.
(iv) n² = the sum of first n odd natural numbers. Ans.

Question 13.
Solution:
(i) False: No. of digits of a perfect square can be even or odd.
(ii) False: Square of a prime number is not a prime number.
(iii) False: It is not always possible.
(iv) False: It is not always possible.
(v) True: The product of two squares is always a perfect square.

Hope given RS Aggarwal Solutions Class 8 Chapter 3 Squares and Square Roots Ex 3B are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1D.

Other Exercises

Question 1.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 1.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 1.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 1.4

Question 2.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 2.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 2.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 2.3

Question 3.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.4
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.5

Question 4.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 4.1

Question 5.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 5.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 5.2

Question 6.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 6.1

Question 7.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.4
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.5

Question 8.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 8.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 8.3

Question 9.
Solution:
(i) The product of a rational number and its reciprocal is 1.
(ii) Zero has no reciprocal.
(iii) The numbers 1 and -1 are their own reciprocal.
(iv) Zero is not the reciprocal of any number.
(v) The reciprocal of a, where a≠0, is \(\\ \frac { 1 }{ a } \)
(vi) The reciprocal of \(\\ \frac { 1 }{ a } \) where a≠0 is a
(vii) The reciprocal of a positive rational number is positive.
(viii) The reciprocal of a negative rational number is negative.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1D are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A

RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 3 Squares and Square Roots Ex 3A.

Other Exercises

Question 1.
Solution:
(i) 441
= 3 x 3 x 7 x 7
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q1.1
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q1.2
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q1.3
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q1.4
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q1.5

Question 2.
Solution:
(i) 1225
= 5 x 5 x 7 x 7
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q2.1
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q2.2
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q2.3
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q2.4

Question 3.
Solution:
(i) Factors of 3675
3 x 5 x 5 x 7 x 7
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q3.1
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q3.2
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q3.3
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q3.4
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q3.5
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q3.6

Question 4.
Solution:
(i) 1575
= 3 x 3 x 5 x 5 x 7
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q4.1
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q4.2
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q4.3
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q4.4
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q4.5
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q4.6

Question 5.
Solution:
The largest two digit number = 99
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q5.1
Finding the square root of 99, we get remainder = 18
∴The greatest two digit number which is a perfect square will be = 99 – 18 = 81

Question 6.
Solution:
The largest 3 digit number = 999
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3A Q6.1
Finding the square root of 999, we get remainder = 38
∴The greatest 3 digit number which is a perfect square = 999 – 38 = 961

Hope given RS Aggarwal Solutions Class 8 Chapter 3 Squares and Square Roots Ex 3A are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C

RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 2 Exponents Ex 2C.

Other Exercises

Objective Questions :
Tick the correct answer in each of the following:

Question 1.
Solution:
Answer = (c)
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q1.1

Question 2.
Solution:
Answer = (d)
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q2.1

Question 3.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q3.1

Question 4.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q4.1

Question 5.
Solution:
Answer = (b)
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q5.1

Question 6.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q6.1

Question 7.
Solution:
Answer = (a)
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q7.1

Question 8.
Solution:
Answer = (a)
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q8.1

Question 9.
Solution:
Answer = (d)
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q9.1

Question 10.
Solution:
Answer = (d)
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q10.1

Question 11.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q11.1

Question 12.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q12.1

Question 13.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q13.1

Question 14.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q14.1

Question 15.
Solution:
3670000 = 3.670000 x 1000000
= 3.67 x 106 (c)

Question 16.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q16.1

Question 17.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2C Q17.1

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RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1G.

Other Exercises

Question 1.
Solution:
Total length of rope = 11 m.
Sum of lengths of two parts
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q1.1

Question 2.
Solution:
Total weight of rice and drum
= \(40\frac { 1 }{ 6 } \) kg
= \(13\frac { 3 }{ 4 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q2.1

Question 3.
Solution:
Total weight of three types of fruits
= \(19\frac { 1 }{ 3 } \) kg
= \(\\ \frac { 58 }{ 3 } \) kg
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q3.1

Question 4.
Solution:
Total earnings = Rs 160
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q4.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q4.2

Question 5.
Solution:
Cost of 1m cloth = Rs \(63\frac { 3 }{ 4 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q5.1

Question 6.
Solution:
Distance covered in 1 hour
= \(60\frac { 2 }{ 5 } \)
= \(\\ \frac { 302 }{ 5 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q6.1

Question 7.
Solution:
Length of rectangular park
= \(36\frac { 3 }{ 5 } \) m
= \(\\ \frac { 183 }{ 5 } \)
and breadth = \(16\frac { 2 }{ 3 } \) = \(\\ \frac { 50 }{ 3 } \) m
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q7.1

Question 8.
Solution:
Side of a square plot = \(8\frac { 1 }{ 2 } \) m
= \(\\ \frac { 17 }{ 2 } \) m
Area = (Side)² = Side x Side
= \(\\ \frac { 17 }{ 2 } \) x \(\\ \frac { 17 }{ 2 } \) m²
= \(\\ \frac { 289 }{ 4 } \) m²
= \(72\frac { 1 }{ 4 } \) m²

Question 9.
Solution:
Cost of 1 litre petrol = Rs \(63\frac { 3 }{ 4 } \)
= Rs \(\\ \frac { 255 }{ 4 } \)
Cost of 34 litres of petrol
= \(\\ \frac { 255 }{ 4 } \) x 34
= \(\\ \frac { 255X17 }{ 2 } \)
= \(\\ \frac { 4335 }{ 2 } \)
= Rs \(2167\frac { 1 }{ 2 } \)

Question 10.
Solution:
Distance covered in 1 hour = 1020 km.
Distance covered in \(4\frac { 1 }{ 6 } \) hours
= 1020 x \(4\frac { 1 }{ 6 } \)
= 1020 x \(\\ \frac { 25 }{ 6 } \) km
= \(\\ \frac { 25500 }{ 6 } \)
= 4250 km. Ans.

Question 11.
Solution:
Cost of \(3\frac { 1 }{ 2 }\) metres cloth
= Rs \(166\frac { 1 }{ 4 }\)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q11.1

Question 12.
Solution:
Total length of piece of chord
= \(71\frac { 1 }{ 2 }\)
No. of pieces = 26
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q12.1

Question 13.
Solution:
Area of a room = \(65\frac { 1 }{ 4 }\) m²
Breadth = \(5\frac { 7 }{ 16 }\) m
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q13.1

Question 14.
Solution:
Product of two fractions = \(9\frac { 3 }{ 5 }\)
= \(\\ \frac { 48 }{ 5 } \)
One fraction = \(9\frac { 3 }{ 7 }\) = \(\\ \frac { 66 }{ 7 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q14.1

Question 15.
Solution:
Let total number of students =1
and no.of boys = \(\\ \frac { 5 }{ 8 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q15.1

Question 16.
Solution:
Let no of pages = 1
Then no. of pages read = \(\\ \frac { 7 }{ 9 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q16.1

Question 17.
Solution:
Total amount, Rita has = Rs 300
Amount spent on notebooks = \(\\ \frac { 1 }{ 3 } \) of 300
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q17.1

Question 18.
Solution:
Total amount earned by Amit = Rs 32000
Amount spent on food = \(\\ \frac { 1 }{ 4 } \) of Rs 32000
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q18.1

Question 19.
Solution:
Let number = 1
Then difference between \(\\ \frac { 3 }{ 5 } \) and \(\\ \frac { 2 }{ 7 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q19.1

Question 20.
Solution:
Let total number of spectators = 1
No. of spectators in covered place = \(\\ \frac { 2 }{ 7 } \) of
1 = \(\\ \frac { 2 }{ 7 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1G Q20.1

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1G are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C

RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 3 Squares and Square Roots Ex 3C.

Other Exercises

Question 1.
Solution:
(23)² = 529
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q1.1

Question 2.
Solution:
(35)² = 1225
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q2.1

Question 3.
Solution:
(52)² = 2704
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q3.1

Question 4.
Solution:
(96)² = 9216
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q4.1

Find the value of each of the following using the diagonal method :

Question 5.
Solution:
(67)² = 4489 Ans.
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q5.1

Question 6.
Solution:
(86)² = 7396 Ans
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q6.1

Question 7.
Solution:
(137)² = 18769 Ans
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q7.1

Question 8.
Solution:
(256)² = 65536 Ans.
RS Aggarwal Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3C Q8.1

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RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A

RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A3

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 2 Exponents Ex 2A.

Other Exercises

Question 1.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A 1
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q1.2

Question 2.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q2.1
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q2.2

Question 3.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q3.1
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q3.2

Question 4.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q4.1
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q4.2

Question 5.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q5.1

Question 6.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q6.1

Question 7.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q7.1

Question 8.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q8.1

Question 9.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q9.1

Question 10.
Solution:
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q10.1

Question 11.
Solution:
Let x be the required number which is multiplied
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q11.1

Question 12.
Solution:
Let x be the required number
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q12.1

Question 13.
Solution:
52x+1 ÷ 25 = 125
RS Aggarwal Class 8 Solutions Chapter 2 Exponents Ex 2A Q13.1

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RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1F

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1F

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1F.

Other Exercises

Question 1.
Solution:
Rational number between \(\\ \frac { 1 }{ 4 } \) and \(\\ \frac { 1 }{ 3 } \)
= \(\\ \frac { 1 }{ 2 } \) \(\left[ \frac { 1 }{ 4 } +\frac { 1 }{ 3 } \right] \)
= \(\\ \frac { 1 }{ 2 } \) \(\left[ \frac { 3+4 }{ 12 } \right] \)
= \(\\ \frac { 1 }{ 2 } \) x \(\\ \frac { 7 }{ 12 } \)
= \(\\ \frac { 7 }{ 24 } \)

Question 2.
Solution:
Solution. Rational number between 2 and 3
= \(\\ \frac { 1 }{ 2 } \)(2 + 3)
= \(\\ \frac { 1 }{ 2 } \) x 5
= \(\\ \frac { 5 }{ 2 } \)

Question 3.
Solution:
Rational number between \(\\ \frac { -1 }{ 3 } \) and \(\\ \frac { 1 }{ 2 } \)
= \(\\ \frac { 1 }{ 2 } \) \(\left[ \frac { -1 }{ 3 } +\frac { 1 }{ 2 } \right] \)
= \(\\ \frac { 1 }{ 2 } \) \(\left[ \frac { -2+3 }{ 6 } \right] \)
= \(\\ \frac { 1 }{ 2 } \) x \(\\ \frac { 1 }{ 6 } \)
= \(\\ \frac { 1 }{ 12 } \)

Question 4.
Solution:
First rational number between -3 and -2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1F Q4.1

Question 5.
Solution:
First rational number between 4 and 5
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1F Q5.1

Question 6.
Solution:
First rational numbers between \(\\ \frac { 2 }{ 3 } \) and \(\\ \frac { 3 }{ 4 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1F Q6.1

Question 7.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1F Q7.1

Question 8.
Solution:
– 1 = \(\\ \frac { -5 }{ 5 } \) and 2 = \(\\ \frac { 10 }{ 5 } \)
12 rational number between – 1 and 2 can be
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1F Q8.1

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1F are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1C.

Other Exercises

Question 1.
Solution:
(i) \(\\ \frac { -2 }{ 5 } \) + \(\\ \frac { 4 }{ 5 } \)
= \(\\ \frac { -2+4 }{ 5 } \) = \(\\ \frac { 2 }{ 5 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 1

Question 2.
Solution:
(i) \(\frac { 3 }{ 4 } +\left( \frac { -3 }{ 5 } \right) \)
\(\frac { 15+\left( -12 \right) }{ 20 } =\frac { 15-12 }{ 20 } =\frac { 3 }{ 20 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 4

Question 3.
Solution:
(i) L.H.S = \(\\ \frac { -12 }{ 5 } \) + \(\\ \frac { 2 }{ 7 } \)
= \(\\ \frac { -84+10 }{ 35 } \) = \(\\ \frac { -74 }{ 35 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 5
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 6
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 7

Question 4.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 8
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 9
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 10
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 11
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 12

Question 5.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 13
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 14

Question 6.
Solution:
We know that additive inverse of \(\\ \frac { a }{ b } \) is \(\\ \frac { -a }{ b } \) and of \(\\ \frac { -a }{ b } \) is \(\\ \frac { a }{ b } \).
Therefore Additive inverse of
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 15
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 16

Question 7.
Solution:
(i) \(\\ \frac { 3 }{ 4 } \) from \(\\ \frac { 1 }{ 3 } \) or \(\\ \frac { 1 }{ 3 } \) – \(\\ \frac { 3 }{ 4 } \)
= \(\\ \frac { 4-9 }{ 12 } \) = \(\\ \frac { -5 }{ 12 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 17
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 18
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 19
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 20

Question 8.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 21
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 22
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 23

Question 9.
Solution:
Sum of two numbers = – 2
one number = \(\\ \frac { -14 }{ 5 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 24

Question 10.
Solution:
Sum of two numbers = \(\\ \frac { -1 }{ 2 } \)
One number = \(\\ \frac { 5 }{ 6 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 25

Question 11.
Solution:
Sum of two numbers = \(\\ \frac { -3 }{ 2 } \)
one number = \(\\ \frac { -5 }{ 8 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 26

Question 12.
Solution:
Sum of two numbers = \(\\ \frac { 5 }{ 7 } \)
One number = – 1
Second number = \(\\ \frac { 5 }{ 7 } \) – ( – 1)
= \(\\ \frac { 5 }{ 7 } \) + \(\\ \frac { 1 }{ 1 } \)
\(\\ \frac { 5+7 }{ 7 } \) = \(\\ \frac { 12 }{ 7 } \)

Question 13.
Solution:
Difference of two numbers = \(\\ \frac { -1 }{ 6 } \)
One number = \(\\ \frac { -2 }{ 3 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 27

Question 14.
Solution:
(i) 0 is the rational number.
(ii) Yes, the difference of two rational numbers is also rational.
(iii) Yes, addition is commutative.
(iv) Yes, addition associative.
(v) No, subtraction is not commutative.
(vi) No, subtraction is not associative.
(vii) The number itself.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1C are helpful to complete your math homework.

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