# 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 :–

Objective Type Questions Mental Maths,

### 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) 19^{2}

(ii) 33^{2}

(iii) 47^{2}

#### 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:

21^{2} = 441

201^{2} = 40401

2001^{2} = 4004001

20001^{2} = 4 – – – 4 – – – 1

200001^{2} = ————–

#### Question -13

Observe the following pattern and find the missing digits:

9^{2} = 81

99^{2} = 9801

999^{2} = 998001

9999^{2} = 99980001

99999^{2} = 9——–8———01

999999^{2} = 9——–0———1

#### Question 14

Observe the following pattern and find the missing digits:

9^{2} = 81

99^{2} = 9801

999^{2} = 998001

9999^{2} = 99980001

99999^{2} = 9——–8———01

999999^{2} = 9——–0———1

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

Squares and Squares Roots

#### 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 11^{2} and 12^{2} 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, m^{2} – 1, m^{2} + 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 11^{2} and 12^{2} 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, m^{2} – 1, m^{2} + 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 25^{2} and 26^{2}?

(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) n^{2} – 1

(b) (n + 1)^{2}

(c) n^{2} + 1

(d) n^{2}

Answer-5

(d) n^{2}

#### 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 unit^{2}, 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 99^{2} and 100^{2}?

#### 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

Thanks