Squares Roots Class-8 ML Aggarwal Solutions ICSE Maths

APC Understanding Mathematics Chapter-3 Solutions

Squares Roots Class-8 ML Aggarwal Solutions for ICSE Maths Chapter-3 Solutions. We provide step by step Solutions of Exercise / lesson-3 Squares and Squares Roots ICSE Class-8th ML Aggarwal Mathematics.

Our Solutions contain all type Questions with Exe-3.1 , Exe-3.2, Exe-3.3, Exe-3.4, Objective Type Questions (including Mental Maths Multiple Choice Questions )Value Based Questions, HOT and Check Your Progress  to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.

Board ICSE
Publications Avichal Publishig Company (APC)
Subject Maths
Class 8 th
Chapter-3 Squares Roots 
Writer ML Aggarwal
Book Name Understanding
Topics Solution of Exe-3.1 , Exe-3.2, Exe-3.3, Exe-3.4, Objective Type Questions (including Mental Maths Multiple Choice Questions )Value Based Questions, HOT and Check Your Progress
Academic Session 2021-2022

Squares Roots Class-8 ML Aggarwal Solutions for ICSE Maths Chapter-3 Solutions


–: Select Topics :–

Exe-3.1 ,

Exe-3.2,

Exe-3.3 ,

Exe-3.4,

Objective Type Questions Mental Maths,

Multiple Choice Questions ,

Value Based Questions,

HOTS

Check Your Progress


ML Aggarwal Class-8 ICSE Maths Squares and Squares Roots Exe-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

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

Question -3

Find the smallest natural number by which 1008 should be multiplied to make it a perfect square.

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


ML Aggarwal Class-8 ICSE Maths Exe-3.2 Squares and Squares Roots 

Question 1

Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.

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

Question- 3

The following numbers are obviously not perfect. Give reason.
(i) 567
(ii) 2453
(iii) 5298
(iv) 46292
(v) 74000

 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

Question -5

How many natural numbers lie between the square of the following numbers?
(i) 12 and 13
(ii) 90 and 91

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

 Question -7

(i) Express 64 as the sum of 8 odd numbers.
(ii) 121 as the sum of 11 odd numbers

Question- 8

Express the following as the sum of two consecutive integers:
(i) 192
(ii) 332
(iii) 472

Question 9

Find the squares of the following numbers without actual multiplication:
(i) 31
(ii) 42
(iii) 86
(iv) 94

Question -10

Find the squares of the following numbers containing 5 in unit’s place:
(i) 45
(ii) 305
(iii) 525

Question 11

Write a Pythagorean triplet whose one number is
(i) 8
(ii) 15
(iii) 63
(iv) 80

Question -12

Observe the following pattern and find the missing digits:
212 = 441
2012 = 40401
20012 = 4004001
200012 = 4 – – – 4 – – – 1
2000012 = ————–

 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

Question 14

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



Squares and Squares Roots
Exercise – 3.3 ML Aggarwal Class-8 ICSE Maths

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

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

Question- 3

Find the square roots of the following numbers by prime factorisation method

(i)
(ii)
(iii)
(iv)

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

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

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

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

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.

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.

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.

Question- 11

The product of two numbers is 7260. If one number is 15 times the other number, find the numbers.

 Question- 12

Find three positive numbers in the ratio 2 : 3 : 5, the sum of whose squares is 950

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


 ML Aggarwal Solutions Squares and Square roots Exercise – 3.4 ICSE Class-8

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

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

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

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

Question- 5

Find the square root of the following fractions by division method:

(i)
(ii)
(iii)

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

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

Question -8

Find the smallest four-digit number which is a perfect square.

Question -9

Find the greatest number of six digits which is a perfect square

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

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.

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?

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?

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.


Objective Type Question Mental Maths ML Aggarwal Class-8 ICSE Maths Squares and Squares Roots Chapter-3 Solutions

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 ………

Answer-1

(i) A number ending in 2, 3, 7, and 8 is never a perfect square.
(ii) On combining two consecutive triangular number, we get a square number.
(iii) If a number has digits 1 or 9 in the unit’s place, then its square ends in 1.
(iv) Sum of the first 10 odd natural numbers is = 100
(v) A number of non-square numbers between 112 and 122 is 12 + 11 – 1 = 22
(vi) Number of zeros in the end of the square of 400 is 0000 (four zeros)
(vii) Square of any odd 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 Pythagorean triplet

Question -2

State whether the following statements are true (T) or false (F):

Answer-2

(i) True

(ii) True

(iii) True

(iv) False

(v) False

(vi) True

(vii) True

(viii) True

(ix) False


Multiple Choice Question (MCQ), ML Aggarwal Class-8 ICSE Maths Squares and Squares Roots Chapter-3 Solutions

Question 3

How many natural numbers lie between 252 and 262?
(a) 49
(b) 50
(c) 51
(d) 52

Answer-3

(b) 50

Question -4

Square of an even number is always
(a) even
(b) odd
(c) even or odd
(d) none of these

Answer-4

(a) even

 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

Answer-5

(d) n2

Question-6

208+ 2304 is equal to
(a) 18
(b) 16
(c) 14
(d) 22

Answer-6

(b) 16

Question -7

√0.0016 is equal to
(a) 0.04
(b) 0.004
(c) 0.4
(d) none of these

Answer-7

(a) 0.04

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

Answer-8

(c) 3

Question -9

√3 ….. is equal to

Answer-9

9/5

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

Answer-10

(c) 2

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

Answer-11

(c) 31 untis

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

Answer-12

(a) 11

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)

Answer-13

(d) (6, 8, 10)

Question -14.
nth triangular number is

(a)
(b)
(c)
(d)

Answer-14

 

Question-15

Given that √1521 = 39, the value of √0.1521+√15.21 is
(a) 42.9
(b) 4.29
(c) 3.51
(d) 35.1

Answer

(b) 4.29


Value Based Question

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?

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?


Higher Order Thinking  Skills ( HOTS ) ML Aggarwal Class-8 ICSE Maths Chapter-3 Squares and Squares Roots

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.

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.

 


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

Question 1

Show that 1089 is a perfect square. Also, find the number whose square is 1089.

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.

Question- 3

Express 121 as the sum of 11 odd numbers

Question- 4

How many numbers lie between 992 and 1002?

Question -5

Write a Pythagorean triplet whose one number is 17.

Question -6

Find the smallest square number which is divisible by each of the numbers 6, 8, 9.

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

Question -8

Find the length of diagonal of a rectangle whose length and breadth are 12 m and 5 m respectively

Question -9

Find the square root of 144 by successive subtraction.

Question- 10

Find the square root of the following numbers by prime factorization:
(i) 5625
(ii) 1521

Question- 11

Find the square root of the following numbers by long division method:
(i) 21904
(ii) 108241

Question- 12

Find the square root of following decimal numbers:
(i) 17.64
(ii) 13.3225

Question -13

Find the square root of the following fractions:

Question -14

Find the least number which must be subtracted from 2311 to make it a perfect square.

Question 15

Find the least number which must be added to 520 to make it a perfect square.

Question -16

Find the greatest number of 5 digits which is a perfect square.

— End of Squares and Square Roots Class-8 ML Solutions :–

Return to –  ML Aggarwal Maths Solutions for ICSE Class -8

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