Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots

Squares and Square Roots Exercise 3A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the square of :
(i) 59
(ii) 63
(iii) 15
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 1

Question 2.
By splitting into prime factors, find the square root of :
(i) 11025
(ii) 396900
(iii) 194481
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 2
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 3

Question 3.
(i) Find the smallest number by which 2592 be multiplied so that the product is a perfect square.
(ii) Find the smallest number by which 12748 be multiplied so that the product is a perfect square?
Solution:
</spanSelina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 4

Question 4.
Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 5
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 6

Question 5.
Find the square root of :
(i) 0.1764
(ii) \(96\frac { 1 }{ 25 }\)
(iii) 0.0169
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 60
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 58
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 59

Question 6.
Evaluate
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 8
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 9
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 10

Question 7.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 11
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 12
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 13
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 14

Question 8.
A man, after a tour, finds that he had spent every day as many rupees as the number of days he had been on tour. How long did his tour last, if he had spent in all ₹ 1,296
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 15

Question 9.
Out of 745 students, maximum are to be arranged in the school field for a P.T. display, such that the number of rows is equal to the number of columns. Find the number of rows if 16 students were left out after the arrangement.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 16

Question 10.
13 and 31 is a strange pair of numbers such that their squares 169 and 961 are also mirror images of each other. Find two more such pairs.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 17

Question 11.
Find the smallest perfect square divisible by 3, 4, 5 and 6.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 18

Question 12.
If √784 = 28, find the value of:
(i) √7.84 + √78400
(ii) √0.0784 + √0.000784
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3A 19

Squares and Square Roots Exercise 3B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the square root of:
(i) 4761
(ii) 7744
(iii) 15129
(iv) 0.2916
(v) 0.001225
(vi) 0.023104
(vii) 27.3529
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 20
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 21
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 22

Question 2.
Find the square root of:
(i) 4.2025
(ii) 531.7636
(iii) 0.007225
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 23
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 24

Question 3.
Find the square root of:
(i) 245 correct to two places of decimal.
(ii) 496 correct to three places of decimal.
(iii) 82.6 correct to two places of decimal.
(iv) 0.065 correct to three places of decimal.
(v) 5.2005 correct to two places of decimal.
(vi) 0.602 correct to two places of decimal
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 25
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 26
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 27

Question 4.
Find the square root of each of the following correct to two decimal places:
(i) \(3\frac { 4 }{ 5 }\)
(ii) \(6\frac { 7 }{ 8 }\)
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 28
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 29

Question 5.
For each of the following, find the least number that must be subtracted so that the resulting number is a perfect square.
(i) 796
(ii) 1886
(iii) 23497
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 30
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 31

Question 6.
For each of the following, find the least number that must be added so that the resulting number is a perfect square.
(i) 511
(ii) 7172
(iii) 55078
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 32
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 33

Question 7.
Find the square root of 7 correct to two decimal places; then use it to find the value of \(\sqrt { \frac { 4+\sqrt { 7 } }{ 4-\sqrt { 7 } } }\) correct to three significant digits.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 34

Question 8.
Find the value of √5 correct to 2 decimal places; then use it to find the square root of \(\sqrt { \frac { 3-\sqrt { 5 } }{ 3+\sqrt { 5 } } }\) correct to 2 significant digits.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 35

Question 9.
Find the square root of:
(i) \(\frac { 1764 }{ 2809 }\)
(ii) \(\frac { 507 }{ 4107 }\)
(iii) \(\sqrt { 108\times 2028 }\)
(iv) 0.01 + √0.0064
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 35
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 37
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 38

Question 10.
Find the square root of 7.832 correct to :
(i) 2 decimal places
(ii) 2 significant digits.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 39

Question 11.
Find the least number which must be subtracted from 1205 so that the resulting number is a perfect square.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 40

Question 12.
Find the least number which must be added to 1205 so that the resulting number is a perfect square.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 41

Question 13.
Find the least number which must be subtracted from 2037 so that the resulting number is a perfect square.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 42

Question 14.
Find the least number which must be added to 5483 so that the resulting number is a perfect square.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3B 43

Squares and Square Roots Exercise 3C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Seeing the value of the digit at unit’s place, state which of the following can be square of a number :
(i) 3051
(ii) 2332
(iii) 5684
(iv) 6908
(v) 50699
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 44

Question 2.
Squares of which of the following numbers will have 1 (one) at their unit’s place :
(i) 57
(ii) 81
(iii) 139
(iv) 73
(v) 64
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 45

Question 3.
Which of the following numbers will not have 1 (one) at their unit’s place :
(i) 322
(ii) 572
(iii) 692
(iv) 3212
(v) 2652
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 46

Question 4.
Square of which of the following numbers will not have 6 at their unit’s place :
(i) 35
(ii) 23
(iii) 64
(iv) 76
(v) 98
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 47

Question 5.
Which of the following numbers will have 6 at their unit’s place :
(i) 262
(ii) 492
(iii) 342
(iv) 432
(v) 2442
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 48

Question 6.
If a number ends with 3 zeroes, how many zeroes will its square have?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 49

Question 7.
If the square of a number ends with 10 zeroes, how many zeroes will the number have?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 50

Question 8.
Is it possible for the square of a number to end with 5 zeroes ? Give reason.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 51

Question 9.
Give reason to show that none of the numbers, given below, is a perfect square.
(i) 2162
(ii) 6843
(iii) 9637
(iv) 6598
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 52

Question 10.
State, whether the square of the following numbers is even or odd?
(i) 23
(ii) 54
(iii) 76
(iv) 75
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 53

Question 11.
Give reason to show that none of the numbers 640, 81000 and 3600000 is a perfect square.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 54

Question 12.
Evaluate:
(i) 372 – 362
(ii) 852 – 842
(iii) 1012 – 1002
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 55

Question 13.
Without doing the actual addition, find the sum of:
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
(ii) 1 + 3 + 5 + 7 + 9 + ……………… + 39 + 41
(iii) 1 + 3 + 5 + 7 + 9 + ………………… + 51 + 53
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 56

Question 14.
Write three sets of Pythagorean triplets such that each set has numbers less than 30.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 3 Squares and Square Roots Ex 3C 57

Selina Concise Mathematics Class 8 ICSE Solutions