Category: CBSE Class 8

RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.1

Other Exercises

• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.1
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.2
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.3
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.4
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.5
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.6
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.7
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.8
• RD Sharma Class 8 Solutions Chapter 3 Squares and Square Roots Ex 3.9

Question 1.
Which of the following numbers are perfect squares ?
(i)484
(ii) 625
(iii) 576
(iv) 941
(v) 961
(vi) 2500
Solution:

Grouping the factors in pairs, we have left no factor unpaired
∴ 484 is a perfect square of 22

∴ Grouping the factors in pairs, we have left no factor unpaired
∴ 625 is a perfect square of 25.

Grouping the factors in pairs, we see that no factor is left unpaired
∴ 576 is a perfect square of 24
(iv) 941 has no prime factors

∴ 941 is not a perfect square.
(v) 961 =31 x 31
Grouping the factors in pairs, we see that no factor is left unpaired
∴ 961 is a perfect square of 31

Grouping the factors in pairs, we see that no factor is left impaired
∴ 2500 is a perfect square of 50 .

Question 2.
Show that each of the following* numbers is a perfect square. Also find the number whose square is the given number in each case :
(i) 1156
(ii) 2025
(iii) 14641
(iv) 4761
Solution:

Grouping the factors in pairs, we see that no factor is left unpaired
∴ 1156 is a perfect square of 2 x 17 = 34

Grouping the factors in pairs, we see that no factor is left unpaired
2025 is a perfect square of 3 x 3 x 5 =45

Grouping the factors in pairs, we see that no factor is left unpaired
∴ 14641 is a perfect square of 11×11 = 121

Grouping the factors in pairs, we see that no factor is left unpaired
∴ 4761 is a perfect square of 3 x 23 = 69

Question 3.
Find the smallest number by which the given number must be multiplied so that the product is a perfect square.
(i) 23805
(ii) 12150
(iii) 7688
Solution:

Grouping the factors in pairs of equal factors, we see that 5 is left unpaird
∴ In order to complete the pairs, we have to multiply 23805 by 5, then the product will be the perfect square.
Requid smallest number = 5
(ii) 12150 = 2 x 3 x 3×3 x 3×3 x 5×5

Grouping the factors in pairs of equal factors, we see that factors 2 and 3 are left unpaired
∴ In order to complete the pairs, we have to multiply 12150 by 2 x 3 =6 i.e., then the product will be the complete square.
∴ Required smallest number = 6

Grouping the factors in pairs of equal factors, we see that factor 2 is left unpaired
∴ In order to complete the pairs we have to multiply 7688 by 2, then the product will be the complete square
∴ Required smallest number = 2

Question 4.
Find the smallest number by which the given number must be divided so that the resulting number is a perfect square.
(i) 14283
(ii) 1800
(iii) 2904
Solution:

Grouping the factors in pairs of equal factors, we see that factors we see that 3 is left unpaired
Deviding by 3, the quotient will the perfect square.

Grouping the factors in pair of equal factors, we see that 2 is left unpaired.
∴ Dividing by 2, the quotient will be the perfect square.

Grouping the factors in pairs of equal factors, we see that 2 x 3 we left unpaired
∴ Dividing by 2 x 3 = 6, the quotient will be the perfect square.

Question 5.
Which of the following numbers are perfect squares ?
11, 12, 16, 32, 36, 50, 64, 79, 81, 111, 121
Solution:
11 is not a perfect square as 11 = 1 x 11
12 is not a perfect square as 12 = 2×2 x 3
16 is a perfect square as 16 = 2×2 x 2×2
32 is not a perfect square as 32 = 2×2 x 2×2 x 2
36 is a perfect square as 36 = 2×2 x 3×3
50 is not a perfect square as 50 = 2 x 5×5
64 is a perfect square as 64 = 2×2 x 2×2 x 2×2
79 is not a perfect square as 79 = 1 x 79
81 is a perfect square as 81 = 3×3 x 3×3
111 is not a perfect square as 111 = 3 x 37
121 is a perfect square as 121 = 11 x 11
Hence 16, 36, 64, 81 and 121 are perfect squares.

Question 6.
Using prime factorization method, find which of the following numbers are perfect squares ?
∴ 189,225,2048,343,441,2916,11025,3549
Solution:

Grouping the factors in pairs, we see that are 3 and 7 are left unpaired
∴ 189 is not a perfect square

Grouping the factors in pairs, we see no factor left unpaired
∴ 225 is a perfect square

Grouping the factors in pairs, we see no factor left unpaired
∴ 2048 is a perfect square

Grouping the factors in pairs, we see that one 7 is left unpaired
∴ 343 is not a perfect square.

Grouping the factors in pairs, we see that no factor is left unpaired
∴ 441 is a perfect square.

Grouping the factors in pairs, we see that no factor is left unpaired
∴ 2916 is a perfect square.

Grouping the factors in pairs, we see that no factor is left unpaired
∴ 11025 is a perfect square.

Grouping the factors in pairs, we see that 3, no factor 7 are left unpaired
∴ 3549 is a perfect square.

Question 7.
By what number should each of the following numbers be multiplied to get a perfect square in each case ? Also, find the number whose square is the new number.
(i) 8820
(ii) 3675
(iii) 605
(iv) 2880
(v) 4056
(vi) 3468
Solution:

Grouping the factors in pairs, we see that 5 is left unpaired
∴ By multiplying 8820 by 5, we get the perfect square and square root of product will be
= 2 x 3 x 5 x 7 = 210

Grouping the factors in pairs, we see that 3 is left unpaired
∴ Multiplying 3675 by 3, we get a perfect square and square of the product will be
= 3 x 5 x 7 = 105

Grouping the factors in pairs, we see that 5 is left unpaired
∴ Multiplying 605 by 5, we get a perfect square and square root of the product will be
= 5 x 11 =55

Grouping the factors in pairs, we see that 5 is left unpaired
∴ Multiplying 2880 by 5, we get the perfect square.
Square rooi of product will be = 2 x 2 * 2 – 3 x 5 = 120

Grouping the factors in pairs, we see that 2 and 3 are left unpaired
∴ Multiplying 4056 by 2 x 3 i.e., 6, we get the perfect square.
and square root of the product will be
= 2 x 2 x 3 x 13 = 156

Grouping the factors in pairs, we see that 3 is left unpaired
∴ Multiplying 3468 by 3 we get a perfect square, and square root of the product will be 2 x 3 x 17 = 102

Grouping the factors in pairs, we see that 2 and 3 are left unpaired
∴ Multiplying 7776 by 2 x 3 or 6 We get a perfect square and square root of the product will be
= 2 x 2 x 2 x 3 x 3 x 3 = 216

Question 8.
By what numbers should each of the following be .divided to get a perfect square in each case ? Also find the number whose square is the new number.
(i) 16562
(ii) 3698
(iii) 5103
(iv) 3174
(v) 1575
Solution:

Grouping the factors in pairs, we see that 2 is left unpaired
∴ Dividing by 2, we get the perfect square and square root of the quotient will be 7 x 13 = 91

Grouping the factors in pairs, we see that 2 is left unpaired,
∴ Dividing 3698 by 2, the quotient is a perfect square
and square of quotient will be = 43

Grouping the factors in pairs, we see that 7 is left unpaired
∴ Dividing 5103 by 7, we get the quotient a perfect square.
and square root of the quotient will be 3 x 3 x 3 = 27

Grouping the factors iq pairs, we see that 2 and 3 are left unpaired
∴ Dividing 3174 by 2 x 3 i.e. 6, the quotient will be a perfect square and square root of the quotient will be = 23

Grouping the factors in pairs, we find that 7 is left unpaired i
∴ Dividing 1575 by 7, the quotient is a perfect square
and square root of the quotient will be = 3 x 5 = 15

Question 9.
Find the greatest number of two digits which is a perfect square.
Solution:
The greatest two digit number = 99 We know, 92 = 81 and 102 = 100 But 99 is in between 81 and 100
∴ 81 is the greatest two digit number which is a perfect square.

Question 10.
Find the least number of three digits which is perfect square.
Solution:
The smallest three digit number =100
We know that 92 = 81, 102 = 100, ll2 = 121
We see that 100 is the least three digit number which is a perfect square.

Question 11.
Find the smallest number by which 4851 must be multiplied so that the product becomes a perfect square.
Solution:
By factorization:

Grouping the factors in pairs, we see that 11 is left unpaired
∴ The least number is 11 by which multiplying 4851, we get a perfect square.

Question 12.
Find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square.
Solution:
By factorization,

Grouping the factors in pairs, we see that 13 is left unpaired
∴ Dividing 28812 by 3, the quotient will be a perfect square.

Question 13.
Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also find the number whose square is the resulting number.
Solution:
By factorization,

Grouping the factors in pairs, we see that one 2 is left unpaired.
∴ Dividing 1152 by 2, we get the perfect square and square root of the resulting number 576, will be 2 x 2 x 2 x 3 = 24

 

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RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.2

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.2

Other Exercises

• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.1
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.2
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.3
• RD Sharma Class 8 Solutions Chapter 2 Powers MCQS

Question 1.
Write each of the following in exponential form :

Solution:

Question 2.
Evaluate :

Solution:

Question 3.
Express each of the following as a rational number in the form \(\frac { p }{ q } :\)

Solution:

Question 4.
Simplify :

Solution:

Question 5.
Express each of the following rational numbers with a negative exponent :

Solution:

Question 6.
Express each of the following rational numbers with a positive exponent :

Solution:

Question 7.
Simplify :

Solution:

Question 8.
By what number should 5^-1 be multiplied so that the product may be equal to (-7)^-1 ?
Solution:

Question 9.
By what number should \({ \left( \frac { 1 }{ 2 } \right) }^{ -1 }\) be multiplied so that the product may be equal to \({ \left( \frac { -4 }{ 7 } \right) }^{ -1 }\) ?
Solution:

Question 10.
By what number should (-15)^-1 be divided so that the quotient may be equal to (-5)^-1 ?
Solution:

Question 11.
By what number should \({ \left( \frac { 5 }{ 3 } \right) }^{ -2 }\) be multiplied so that the product may be \({ \left( \frac { 7 }{ 3 } \right) }^{ -1 }\) ?
Solution:

Question 12.
Find x, if

Solution:

Question 13.

Solution:

Question 14.
Find the value of x for which 5^2x + 5^-3 = 5⁵.
Solution:

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RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6

Other Exercises

• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.1
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.2
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

Question 1.
Verify the property : x x y = y x x by taking :

Solution:

Question 2.
Verify the property : x x (y x z) = (x x y) x z by taking :

Solution:

Question 3.
Verify the property :xx(y + 2) = xxy + x x z by taking :

Solution:

Question 4.
Use the distributivity of multiplication of rational numbers over their addition to simplify :

Solution:

Question 5.
Find the multiplicative inverse (reciprocal) of each of the following rational numbers :


Solution:

Question 6.
Name the property of multiplication of rational numbers illustrated by the following statements :

Solution:

Question 7.
(i) The product of two positive rational numbers is always______.
(ii) The product of a positive rational number and a negative rational number is always________.
(iii) The product of two negative rational numbers is always________.
(iv) The reciprocal of a positive rational number is________.
(v) The reciprocal of a negative rational number is________.
(vi) Zero has reciprocal. The product of a rational number and its reciprocal is______.
(viii) The numbers and are their own reciprocals______.
(ix) If a is reciprocal of b, then the reciprocal of b is______.
(x) The number 0 is the reciprocal of any number______.
(xi) Reciprocal of \(\frac { 1 }{ a }\), a≠ 0 is______.
(xii) (17 x 12)^-1 = 17^-1 x________ .

Solution:
The product of two positive rational numbers is always positive.
(ii) The product of a positive rational number and a negative rational number is always negative.
(iii) The product of two negative rational numbers is always positive.
(iv) The reciprocal of a positive rational number is positive.
(v) The reciprocal of a negative rational number is negative.
(vi) Zero has no reciprocal.
(vii) The product of a rational number and its reciprocal is 1.
(viii)The numbers 1 and -1 are their own reciprocals.
(ix) If a is reciprocal of b, then the reciprocal of b is a.
(x) The number 0 is not the reciprocal of any number.
(xi) Reciprocal of \(\frac { 1 }{ a }\), a≠ 0 is a.
(xii) (17 x 12)^-1 = 17^-1 x________ .

Question 8.
Fill in the blanks :


Solution:
Fill in the blanks :

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RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.3

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.3

Other Exercises

• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.1
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.2
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.3
• RD Sharma Class 8 Solutions Chapter 2 Powers MCQS

Question 1.
Express the following numbers in standard form :
(i) 6020000000000000
(ii) 0.00000000000942
(iii) 0.00000000085
(iv) 846 X 10⁷
(v) 3759 x 10^-4
(vi) 0.00072984
(vii) 0.000437 x 10⁴ 
(Viii) 4 + 100000
Solution:

Question 2.
Write the following numbers in the usual form :
(i) 4.83 x 10⁷
(ii) 3.02 x 10^-6
(iii) 4.5 x 10⁴
(iv) 3 x 10^-8
(v) 1.0001 x 10⁹
(vi) 5.8 x 10²
(vii) 3.61492 x 10⁶
(viii) 3.25 x 10^-7
Solution:

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RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.1

Other Exercises

• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.1
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.2
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.3
• RD Sharma Class 8 Solutions Chapter 2 Powers MCQS

Question 1.
Express each of the following as a rational number of the form \(\frac { p }{ q } ,\) where p and q are integers and q≠ 0 :

Solution:

Question 2.
Find the values of each of the following

Solution:

Question 3.
Find the values of each of the following :

Solution:

Question 4.
Simplify :

Solution:

Question 5.
Simplify :


Solution:

Question 6.
By what number should 5^-1 be multiplied so that the product may be equal to(-7)^-1 ?
Solution:

Question 7.
By what number should \({ \left( \frac { 1 }{ 2 } \right) }^{ -1 }\) multiplied so that the product many be equal to \({ \left( \frac { -4 }{ 7 } \right) }^{ -1 }\)
Solution:

Question 8.
By what number should (-15)^-1 be divided so that the quotient may be equal to (-5)^-1 ?
Solution:

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RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7

Other Exercises

• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.1
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.2
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

Question 1.
Divide :

Solution:

Question 2.
Find the value and express as a rational number in standard form :

Solution:

Question 3.
The product of two rational numbers is15. If one of the numbers is -10, find the other.
Solution:

Question 4.
The product of two rational numbers is\(\frac { -9 }{ 8 }\) if one of the numbers is \(\frac { -4 }{ 15 }\), find other.
Solution:

Question 5.
By what number should we multiply \(\frac { -1 }{ 6 }\) so that the product may be \(\frac { -23 }{ 9 }\) ?
Solution:

Question 6.
By what number should we multiply \(\frac { -15 }{ 28 }\) so that the product may be \(\frac { -5 }{ 7 }\) ?
Solution:

Question 7.
By what number should we multiply \(\frac { -8 }{ 13 }\) so that the product may be 24 ?
Solution:

Question 8.
Bv what number should \(\frac { -3 }{ 4 }\) multiplied in order to produce \(\frac { 2 }{ 3 }\) ?
Solution:

Question 9.
Find (x +y) + (x – y), if

Solution:

Question 10.
The cost of 7 \(\frac { 2 }{ 3 }\) metres of rope is Rs 12 \(\frac { 3 }{ 4 }\).Find its cost per metre.
Solution:

Question 11.
The cost of 2 \(\frac { 1 }{ 3 }\) metres of cloth is Rs. 75 \(\frac { 1 }{ 4 }\)Find the cost of cloth per metre.
Solution:

Question 12.
By what number should \(\frac { -33 }{ 16 }\) be divided to get \(\frac { -11 }{ 4 }\) ?
Solution:

Question 13.
Divide the sum of \(\frac { -13 }{ 5 }\) and \(\frac { 12 }{ 7 }\) by the product of \(\frac { -31 }{ 7 }\) and \(\frac { -1 }{ 2 }\).
Solution:

Question 14.
Divide the sum of \(\frac { 65 }{ 12 }\) and \(\frac { 12 }{ 7 }\) bv their difference.
Solution:

Question 15.
If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser ?
Solution:

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RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

Other Exercises

• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.1
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.2
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

Question 1.
Find a rational number between -3 and 1.
Solution:

Question 2.
Find any five rational number less than 1.
Solution:

Question 3.
Find four rational numbers between \(\frac { -2 }{ 9 }\) and \(\frac { 5 }{ 9 }\) .
Solution:

Question 4.
Find two rational numbers between \(\frac { 1 }{ 5 }\) and \(\frac { 1 }{ 2 }\) .
Solution:

Question 5.
Find ten rational numbers between \(\frac { 1 }{ 4 }\) and \(\frac { 1 }{ 2 }\) .
Solution:

Question 6.
Find ten rational numbers between \(\frac { -2 }{ 5 }\) and \(\frac { 1 }{ 2 }\) .
Solution:

Question 7.
Find ten rational numbers between \(\frac { 3 }{ 5 }\) and \(\frac { 3 }{ 4 }\) .
Solution:

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RD Sharma Class 8 Solutions Chapter 2 Powers MCQS

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 2 Powers MCQS

Other Exercises

• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.1
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.2
• RD Sharma Class 8 Solutions Chapter 2 Powers Ex 2.3
• RD Sharma Class 8 Solutions Chapter 2 Powers MCQS

Choose the correct alternative in each of the following :

Question 1.
Square of \(\left( \frac { -2 }{ 3 } \right)\)

Solution:

Question 2.
Cube of \(\frac { -1 }{ 2 }\) is

Solution:

Question 3.
Which of the following is not equal to

Solution:

Question 4.
Which of the following in not reciprocal of

Solution:

Question 5.
Which of the following numbers is not equal to \(\frac { -8 }{ 27 }\) ?

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.
For any two non-zero rational numbers a and b,a⁴+b⁴ is equal to
(a) (a + b)¹ 
(b) (a + b)⁰
(c) (a + b)⁴
(d) (a + b)⁸
Solution:
(c) {∵ a⁴ + b⁴ = (a + b)⁴}

Question 16.
For any two rational numbers a and b, a⁵ x b⁵ is equal to
(a) (a x b)⁰
(b) (a x b)¹⁰
(c) (a x b)⁵
(d) (a x b)²⁵
Solution:
(c) {∵ a⁵ x b⁵ = (a x b)⁵}

Question 17.
For a non-zero rational number a, a⁷ + a¹² is equal to
(a) a⁵
(b) a^-19
(c) a-⁵
(d) a¹⁹
Solution:
(c) {a⁵ a¹² = a^7-12 =a^-5}

Question 18.
For a non-zero rational number a, (a³)^-2 is equal to
(a) a⁶
(b) a^-6
(c) a^-9
(d) a¹
Solution:
(b) {(a³)^-2 = a^{3 x (-2)}= a⁶}

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RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5

Other Exercises

• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.1
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.2
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

Question 1.
Multiply:

Solution:

Question 2.
Multiply:

Solution:

Question 3.
Simplify each of the following and express the result as a rational number in standard form :

Solution:

Question 4.
Simplify :


Solution:

Question 5.
Simplify :

Solution:

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RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4

Other Exercises

• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.1
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.2
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

Question 1.
Simplify each of the following and write as a rational number of the form :

Solution:

Question 2.
Express each of the following as a rational number of the form \(\frac { p }{ q }\):


Solution:

Question 3.
Simplify :

Solution:

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RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3

Other Exercises

• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.1
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.2
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.4
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.5
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.6
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.7
• RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.8

Question 1.
Subtract the first rational number from the second in each of the following :



Solution:

Question 2.
Evaluate each of the following :

Solution:

Question 3.
The sum of two numbers is \(\frac { 5 }{ 9 }\). If one of the numbers is \(\frac { 1 }{ 3 }\), find the other.
Solution:

Question 4.
The sum of two numbers is \(\frac { -1 }{ 3 }\). If one of the numbers is \(\frac { -12 }{ 3 }\), find the other.
Solution:

Question 5.
The sum of two numbers is \(\frac { -4 }{ 3 }\). If one of the number is -5, find the
Solution:

Question 6.
The sum of two rational numbers is -8. If one of the numbers is \(\frac { -15 }{ 7 }\) find the other.
Solution:

Question 7.
What should be added to so as to \(\frac { -7 }{ 8 }\) get \(\frac { 5 }{ 9 }\) ?
Solution:

Question 8.
What number should be added to \(\frac { -5 }{ 11 }\) so as to get \(\frac { 26 }{ 3 }\) ?
Solution:

Question 9.
What number should be added to \(\frac { -5 }{ 7 }\) to get \(\frac { -2 }{ 3 }\) ?
Solution:

Question 10.
What number should be subtracted from \(\frac { -5 }{ 3 }\) to get \(\frac { 5 }{ 6 }\) ?
Solution:

Question 11.
What number should be subtracted from \(\frac { 3 }{ 7 }\) to get \(\frac { 5 }{ 4 }\) ?
Solution:

Question 12.
What should be added to \(\left( \frac { 2 }{ 3 } +\frac { 3 }{ 5 } \right)\) to get \(\frac { -12 }{ 15 }\) ?
Solution:

Question 13.
What should be added to \(\left( \frac { 1 }{ 2 } +\frac { 1 }{ 3 } +\frac { 1 }{ 5 } \right)\) to get 3 ?
Solution:

Question 14.
What should be subtracted from \(\left( \frac { 3 }{ 4 } -\frac { 2 }{ 3 } \right)\) to get \(\frac { -1 }{ 6 }\) ?
Solution:

Question 15.
Fill in the blanks :

Solution:

Hope given RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1.3 are helpful to complete your math homework.

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