Question 1: What could be the possible ‘one’s’ digits of the square root of each of the following numbers?

(i) 9801

**Answer:** 1 and 9.**Explanation:** Since 1^{2} and 9^{2} give 1 at unit’s place, so these are the possible values of unit digit of the square root.

(ii) 99856

**Answer:** 4 and 6**Explanation:** Since, 4^{2 }= 16 and 6^{2 }= 36, hence, 4 and 6 are possible digits

(iii) 998001

**Answer:** 1 and 9

(iv) 657666025

**Answer:** 5**Explanation:** Since, 5^{2 }= 25, hence 5 is possible.

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

(i) 153 (ii) 257 (iii) 408 (iv) 441

**Answer:** (i) 153 (ii) 257 (iii) 408**Explanation:** Since, (i), (ii) and (iii) are surely not be perfect square as these numbers end with 3, 7 and 8. A number can be a perfect square if it ends with 0, 1, 4, 5, 6, 9 only

Question 3: Find the square roots of 100 and 169 by the method of repeated subtraction.

**Answer:** Square root of 100 by Repeated subtraction:

1. 100 - 1 = 99

2. 99 - 3 = 96

3. 96 - 5 = 91

4. 91 -7 = 84

5. 84 - 9 = 75

6. 75 - 11 = 64

7. 64 - 13 = 51

8. 51 - 15 = 36

10. 19 - 19 = 0

We get 0 at 10th step. Thus, 10 is the square root of 100.

Square root of 169 by Repeated subtraction:

1. 169 - 1 = 168

2. 168 - 3 = 165

3. 165 - 5 = 160

4. 160 - 7 = 153

5. 153 - 9 = 144

6. 144 - 11 = 133

7. 133 - 13 = 120

8. 120 - 15 = 105

9. 105 - 17 = 88

10. 88 - 19 = 69

11. 69 - 21 = 48

12. 48 - 23 = 25

13. 25 - 25 = 0

We get 0 at 13th step. Thus 13 is the square root of 169

Question 4: Find the square roots of the following numbers by the Prime Factorisation Method.

(i) 729

Thus, Answer = 27

(ii) 400

Thus, Answer = 20

(iii) 1764

**Answer:**

Thus, Answer = 42

(iv) 4096

**Answer:**

Thus, Answer = 64

(v) 7744

**Answer:**

Thus, Answer = 88

(vi) 9604

**Answer:**

Thus, Answer = 98

(vii) 5929

**Answer:**

Thus, Answer = 77

(viii) 9216

**Answer:**

Thus, Answer = 96

(ix) 529

**Answer:**

Thus, Answer = 23

(x) 8100

**Answer:**

Thus, Answer = 90

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