ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1

Question 1.
Which of the following numbers are not perfect cubes? Give reasons in support of your answer:
(i) 648
(ii) 729
(iii) 8640
(iv) 8000
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 3

Question 2.
Show that each of the following numbers is a perfect cube. Also, find the number whose cube is the given number:
(i) 1728
(ii) 5832
(iii) 13824
(iv) 35937
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 4
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 6
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 7

Question 3.
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
(i) 243
(ii) 3072
(iii) 11979
(iv) 19652
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 8
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 9
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 10

Question 4.
Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:
(i) 1536
(ii) 10985
(iii) 28672
(iv) 13718
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 11
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 12
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 13

Question 5.
Rahul makes a cuboid of plasticine of sides 3 cm × 3 cm × 5 cm. How many such cuboids will he need to form a cube?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 14

Question 6.
Find the volume of a cubical box whose surface area is 486 cm2.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 15

Question 7.
Which of the following are cubes of even natural numbers or odd natural numbers:
(i) 125
(ii) 512
(iii) 1000
(iv) 2197
(v) 4096
(vi) 6859
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 16

Question 8.
Write the ones digit of the cube of each of the following numbers:
(i) 231
(ii) 358
(iii) 419
(iv) 725
(v) 854
(vi) 987
(vii) 752
(viii) 893
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 17

Question 9.
Find the cubes of the following numbers:
(i) 13
(ii) \(3 \frac{1}{5}\)
(iii) \(-5 \frac{1}{7}\)
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1 18

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress

Question 1.
Show that 1089 is a perfect square. Also, find the number whose square is 1089.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 1

Question 2.
Find the smallest number which should be multiplied by 3675 to make it a perfect square. Also, find the square root of this perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 2

Question 3.
Express 121 as the sum of 11 odd numbers.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 3

Question 4.
How many numbers lie between 992 and 1002?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 4

Question 5.
Write a Pythagorean triplet whose one number is 17.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 5

Question 6.
Find the smallest square number which is divisible by each of the numbers 6, 8, 9.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 6

Question 7.
In an auditorium, the number of rows is equal to a number of chairs in each row. If the capacity of the auditorium is 1764. Find the number of chairs in each row.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 7

Question 8.
Find the length of diagonal of a rectangle whose length and breadth are 12 m and 5 m respectively.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 8

Question 9.
Find the square root of 144 by successive subtraction.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 9

Question 10.
Find the square root of the following numbers by prime factorisation:
(i) 5625
(ii) 1521
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 10

Question 11.
Find the square root of the following numbers by long division method:
(i) 21904
(ii) 108241
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 11

Question 12.
Find the square root of following decimal numbers:
(i) 17.64
(ii) 13.3225
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 12

Question 13.
Find the square root of the following fractions:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 13
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 14
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 15

Question 14.
Find the least number which must be subtracted from 2311 to make it a perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 16

Question 15.
Find the least number which must be added to 520 to make it a perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 17

Question 16.
Find the greatest number of 5 digits which is a perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Check Your Progress 18

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A number ending in ……… is never a perfect square.
(ii) On combining two consecutive triangular number, we get a ………
(iii) If a number has digits ……… in the unit’s place, then its square ends in 1.
(iv) Sum of the first 10 odd natural numbers is ………
(v) A number of non-square numbers between 112 and 122 is ………
(vi) Number of zeros in the end of the square of 400 is ………
(vii) Square of any ……… number can be expressed as the sum of two consecutive natural numbers.
(viii)For a natural number m > 1, (2m, m2 – 1, m2 + 1) is called ………
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 1

Question 2.
State whether the following statements are true (T) or false (F):
(i) All-natural numbers are not perfect squares.
(ii) A perfect square can never be expressed as the product of pairs of equal prime factors.
(iii) A number having 2,3,7 or 8 at its unit place is never a square number.
(iv) A number having 0, 1, 4, 5, 6 or 9 at its unit place is always a square number.
(v) A number ending in an even number of zeros is always a perfect square.
(vi) Square of an odd number is always an odd number.
(vii) 1, 3, 6, 10, 15, are called triangular numbers.
(viii)There are 2n non-square numbers between the squares of consecutive numbers n and (n + 1).
(ix) (4, 6, 8) is a Pythagorean triplet.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 2

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 15):
Question 3.
How many natural numbers lie between 252 and 262?
(a) 49
(b) 50
(c) 51
(d) 52
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 3

Question 4.
Square of an even number is always
(a) even
(b) odd
(c) even or odd
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 4

Question 5.
1+ 3 + 5 + 7 + ……….. up to n terms is equal to
(a) n2 – 1
(b) (n + 1)2
(c) n2 + 1
(d) n2
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 5

Question 6.
\(\sqrt{208+\sqrt{2304}}\) is equal to
(a) 18
(b) 16
(c) 14
(d) 22
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 6

Question 7.
\(\sqrt{0.0016}\) is equal to
(a) 0.04
(b) 0.004
(c) 0.4
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 7

Question 8.
The smallest number by which 75 should be divided to make it a perfect square is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 8

Question 9.
\(\sqrt{3 \frac{6}{25}}\) is equal to
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 9
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 10

Question 10.
The smallest number by which 162 should be multiplied to make it a perfect square is
(a) 4
(b) 3
(c) 2
(d) 1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 11

Question 11.
If the area of a square field is 961 unit2, then the length of its side is
(a) 29 units
(b) 41 units
(c) 31 untis
(d) 39 units
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 12

Question 12.
The smallest number that should be subtracted from 300 to make it a perfect square is
(a) 11
(b) 12
(c) 13
(d) 14
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 13

Question 13.
If one number of the Pythagorean triplet is 6, then the triplet is
(a) (4, 5, 6)
(b) (5, 6, 7)
(c) (6, 7, 8)
(d) (6, 8, 10)
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 14

Question 14.
nth triangular number is
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 15
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 16

Question 15.
Given that \(\sqrt{1521}\) = 39, the value of \(\sqrt{0.1521}+\sqrt{15.21}\) is
(a) 42.9
(b) 4.29
(c) 3.51
(d) 35.1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 17

Value Based Questions
Question 1.
In a school, students of class VIII collected ₹9216 to give a donation to an NGO working for the education of poor children. If each student donated as many rupees as the number of students in class VIII. Find the number of students in class VIII.
Why should we donate money for the education of poor children? What values are being promoted?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 18

Question 2.
A person wants to plant 2704 medicinal plants with a board depicting the diseases in which that can be used. He planted these in the form of rows. If each row contains as many plants as the number of rows, then find the number of rows.
Why should we plant medicinal plants? What values are being promoted?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 19

Higher Order Thinking Skills (Hots)
Question 1.
A square field is to be ploughed. Ramu get it ploughed in ₹34560 at the rate of ₹15 per sq. m. Find the length of side of square field.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 20

Question 2.
Lalit has some chocolates. He distributed these chocolates among 13 children in such a way that he gave one chocolate to first child, 3 chocolates to the second child, 5 chocolates to third and so on. Find the number of chocolates Lalit had.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Objective Type Questions 21

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4

Question 1.
Find the square root of each of the following by division method:
(i) 2401
(ii) 4489
(iii) 106929
(iv) 167281
(v) 53824
(vi) 213444
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 3

Question 2.
Find the number of digits in the square root of each of the following (without any calculation):
(i) 81
(ii) 169
(iii) 4761
(iv) 27889
(v) 525625
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 4

Question 3.
Find the square root of the following decimal numbers by division method:
(i) 51.84
(ii) 42.25
(iii) 18.4041
(iv) 5.774409
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 5

Question 4.
Find the square root of the following numbers correct to two decimal places:
(i) 645.8
(ii) 107.45
(iii) 5.462
(iv) 2
(v) 3
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 6
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 7
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 8

Question 5.
Find the square root of the following fractions by division method:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 9
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 10
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 11

Question 6.
Find the least number which must be subtracted from each of the following numbers to make them a perfect square. Also find the square root of the perfect square number so obtained:
(i) 2000
(ii) 984
(iii) 8934
(iv) 11021
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 12
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 13

Question 7.
Find the least number which must be added to each of the following numbers to make them a perfect square. Also find the square root of the perfect square number so obtained:
(i) 1750
(ii) 6412
(iii) 6598
(iv) 8000
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 14
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 15
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 16

Question 8.
Find the smallest four-digit number which is a perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 17

Question 9.
Find the greatest number of six digits which is a perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 18

Question 10.
In a right triangle ABC, ∠B = 90°.
(i) If AB = 14 cm, BC = 48 cm, find AC.
(ii) If AC = 37 cm, BC = 35 cm, find AB.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 19
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 20

Question 11.
A gardener has 1400 plants. He wants to plant these in such a way that the number of rows and number of columns remains the same. Find the minimum number of plants he needs more for this.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 21

Question 12.
There are 1000 children in a school. For a P.T. drill they have to stand in such a way that the number of rows is equal to a number of columns. How many children would be left out in this arrangement?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 22

Question 13.
Amit walks 16 m south from his house and turns east to walk 63 ra to reach his friend’s house. While returning, he walks diagonally from his friend’s house to reach back to his house. What distance did he walk while returning?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 23

Question 14.
A ladder 6 m long leaned against a wall. The ladder reaches the wall to a height of 4.8 m. Find the distance between the wall and the foot of the ladder.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.4 24

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3

Question 1.
By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect squares or not? If the number is a perfect square then find its square root:
(i) 121
(ii) 55
(iii) 36
(iv) 90
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 3

Question 2.
Find the square roots of the following numbers by prime factorisation method:
(i) 784
(ii) 441
(iii) 1849
(iv) 4356
(v) 6241
(vi) 8836
(vii) 8281
(viii) 9025
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 4
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 6
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 7

Question 3.
Find the square roots of the following numbers by prime factorisation method:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 8
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 9
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 10
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 11
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 12

Question 4.
For each of the following numbers, find the smallest natural number by which it should be multiplied so as to get a perfect square. Also, find the square root of the square number so obtained:
(i) 588
(ii) 720
(iii) 2178
(iv) 3042
(v) 6300
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 13
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 14
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 15
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 16

Question 5.
For each of the following numbers, find the smallest natural number by which it should be divided so that this quotient is a perfect square. Also, find the square root of the square number so obtained:
(i) 1872
(ii) 2592
(iii) 3380
(iv) 16224
(v) 61347
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 17
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 18
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 19
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 20

Question 6.
Find the smallest square number that is divisible by each of the following numbers:
(i) 3, 6, 10, 15
(ii) 6, 9, 27, 36
(iii) 4, 7, 8, 16
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 21
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 22

Question 7.
4225 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 23

Question 8.
The area of a rectangle is 1936 sq. m. If the length of the rectangle is 4 times its breadth, find the dimensions of the rectangle.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 24

Question 9.
In a school a P.T. teacher wants to arrange 2000 students in the form of rows and columns for P.T. display. If the number of rows is equal to number of columns and 64 students could not be accommodated in this arrangement. Find the number of rows.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 25

Question 10.
In a school, the students of class VIII collected ₹2304 for a picnic. Each student contributed as mdny rupees as the number of students in the class. Find the number of students in the class.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 26

Question 11.
The product of two numbers is 7260. If one number is 15 times the other number, find the numbers.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 27

Question 12.
Find three positive numbers in the ratio 2 : 3 : 5, the sum of whose squares is 950.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 28

Question 13.
The perimeter of two squares is 60 metres and 144 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.3 29

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2

Question 1.
Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 1

Question 2.
What will be the unit digit of the squares of the following numbers?
(i) 951
(ii) 502
(iii) 329
(iv) 643
(v) 5124
(vi) 7625
(vii) 68327
(viii) 95628
(ix) 99880
(x) 12796
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 2

Question 3.
The following numbers are obviously not perfect. Give reason.
(i) 567
(ii) 2453
(iii) 5298
(iv) 46292
(v) 74000
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 3

Question 4.
The square of which of the following numbers would be an odd number or an even number? Why?
(i) 573
(ii) 4096
(iii) 8267
(iv) 37916
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 4

Question 5.
How many natural numbers lie between the square of the following numbers?
(i) 12 and 13
(ii) 90 and 91
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 5

Question 6.
Without adding, find the sum.
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 6

Question 7.
(i) Express 64 as the sum of 8 odd numbers.
(ii) 121 as the sum of 11 odd numbers.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 7

Question 8.
Express the following as the sum of two consecutive integers:
(i) 192
(ii) 332
(iii) 472
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 8
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 9

Question 9.
Find the squares of the following numbers without actual multiplication:
(i) 31
(ii) 42
(iii) 86
(iv) 94
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 10

Question 10.
Find the squares of the following numbers containing 5 in unit’s place:
(i) 45
(ii) 305
(iii) 525
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 11

Question 11.
Write a Pythagorean triplet whose one number is
(i) 8
(ii) 15
(iii) 63
(iv) 80
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 12
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 13

Question 12.
Observe the following pattern and find the missing digits:
212 = 441
2012 = 40401
20012 = 4004001
200012 = 4 – – – 4 – – – 1
2000012 = ————–
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 14

Question 13.
Observe the following pattern and find the missing digits:
92 = 81
992 = 9801
9992 = 998001
99992 = 99980001
999992 = 9——–8———01
9999992 = 9——–0———1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 15

Question 14.
Observe the following pattern and find the missing digits:
72 = 49
672 = 4489
6672 = 444889
66672 = 44448889
666672 = 4 ———–8 ————– 9
6666672 = 4———–8————8 –
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.2 16

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1

Question 1.
Which of the following natural numbers are perfect squares? Give reasons in support of your answer.
(i) 729
(ii) 5488
(iii) 1024
(iv) 243
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 1
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 3
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 4

Question 2.
Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number.
(i) 1296
(ii) 1764
(iii) 3025
(iv) 3969
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 6
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 7

Question 3.
Find the smallest natural number by which 1008 should be multiplied to make it a perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 8

Question 4.
Find the smallest natural number by which 5808 should be divided to make it a perfect square. Also, find the number whose square is the resulting number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 3 Squares and Square Roots Ex 3.1 9

ML Aggarwal Class 8 Solutions for ICSE Maths