Table of Contents

Toggle## Class 8, Maths, Chapter 6, Exercise 6.3, Solutions

**Q.****1. What could be the possible ‘one’s’ digits of the square root of each of the following numbers?**

**(i) 9801 **

**(ii) 99856 **

**(iii) 998001 **

**(iv) 657666025**

**Ans:**

(i) 9801 = 1 or 9

(ii) 99856 = 4 or 6

(iii) 998001 = 1 or 9

(iv) 657666025 = 5

**Q.****2. Without doing any calculation, find the numbers which are surely not perfect squares.**

**(i) 153 **

**(ii) 257 **

**(iii) 408 **

**(iv) 441**

**Ans:**

(i) 153 = last digit 3, not perfect square number.

(ii) 257 = last digit 7, not perfect square number.

(iii) 408 = last digit 8, not perfect square number.

(iv) 441= = last digit __1, perfect square number__.

**Q.****3. Find the square roots of 100 and 169 by the method of repeated subtraction.**

**Ans:**

**(1) The square root of 100 can be obtained by the method of repeated subtraction as:**

(i) 100 – 1 = 99

(ii) 99 – 3 = 96

(iii) 96 – 5 = 91

(iv) 91 – 7 = 84

(v) 84 – 9 = 75

(vi) 75 – 11= 64

(vii) 64 – 13 = 51

(viii) 51 – 15 = 36

(ix) 36 – 17 = 19

(x) 19 – 19 = 0

Here, we obtained 0 at 10^{th} step

Therefore, $\sqrt{\mathsf{100}}\mathsf{=10}$

**(2) The square root of 169 can be obtained by the method of repeated subtraction as:**

(i) 169 – 1 = 168

(ii) 168 – 3 = 165

(iii) 165 – 5 = 160

(iv) 160 – 7 = 153

(v) 153 – 9 = 144

(vi) 144 – 11 = 133

(vii) 133 – 13 = 120

(viii) 120 – 15 = 105

(ix) 105 – 17 = 88

(x) 88 – 19 = 69

(xi) 69 – 21 = 48

(xii) 48 – 23 = 25

(xiii)25 – 25 = 0

Here, we obtained 0 at 13^{th} step

Hence, $\sqrt{\mathsf{169}}\mathsf{=13}$

**Q.****4. Find the square roots of the following numbers by the Prime Factorisation Method.**

**(i) 729 **

**(ii) 400 **

**(iii) 1764 **

**(iv) 4096**

**(v) 7744 **

**(vi) 9604 **

**(vii) 5929 **

**(viii) 9216**

**(ix) 529 **

**(x) 8100**

**Ans:**

**Q.****5. For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.**

**(i) 252 **

**(ii) 180**

**(iii) 1008**

**(iv) 2028**

**(v) 1458**

**(vi) 768**

**Ans:**

**Q.6. For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.**

**(i) 252 **

**(ii) 2925**

**(iii) 396**

**(iv) 2645**

**(v) 2800**

**(vi) 1620**

**Ans:**

**Q.****7. The students of Class VIII of a school donated ****₹**** 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class. **

**Q.****8. 2025 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.**

**Q.****9. Find the ****smallest square number that is divisible by each of the numbers 4, 9 and 10.**

**Q.****10. Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.**

## NCERT Solutions For Class 8 Maths Chapter 6, Squares and Square Roots (All Exercises)

**Class 8, Maths, Chapter 6, Squares and Square roots **

**Class 8, Maths, Chapter 6, Squares and Square roots, Exercise 6.1**

**Class 8, Maths, Chapter 6, Squares and Square roots, Exercise 6.2**

**Class 8, Maths, Chapter 6, Squares and Square roots, Exercise 6.3** **← You are here**

**Class 8, Maths, Chapter 6, Squares and Square roots, Exercise 6.4**