## 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:

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:

Question 3.

The following numbers are obviously not perfect. Give reason.

(i) 567

(ii) 2453

(iii) 5298

(iv) 46292

(v) 74000

Solution:

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:

Question 5.

How many natural numbers lie between the square of the following numbers?

(i) 12 and 13

(ii) 90 and 91

Solution:

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:

Question 7.

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

(ii) 121 as the sum of 11 odd numbers.

Solution:

Question 8.

Express the following as the sum of two consecutive integers:

(i) 19^{2}

(ii) 33^{2}

(iii) 47^{2}

Solution:

Question 9.

Find the squares of the following numbers without actual multiplication:

(i) 31

(ii) 42

(iii) 86

(iv) 94

Solution:

Question 10.

Find the squares of the following numbers containing 5 in unit’s place:

(i) 45

(ii) 305

(iii) 525

Solution:

Question 11.

Write a Pythagorean triplet whose one number is

(i) 8

(ii) 15

(iii) 63

(iv) 80

Solution:

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} = ————–

Solution:

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

Solution:

Question 14.

Observe the following pattern and find the missing digits:

7^{2} = 49

67^{2} = 4489

667^{2} = 444889

6667^{2} = 44448889

66667^{2} = 4 ———–8 ————– 9

666667^{2} = 4———–8————8 –

Solution: