1 (i) 9801

Answer: 1 and 9.

Explanation: Since 12 and 92 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, 42 = 16 and 62 = 36, hence, 4 and 6 are possible digits

(iii) 998001

Answer: 1 and 9

(iv) 657666025

Answer: 5

Explanation: Since, 52 = 25, hence 5 is possible.

2 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

3 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 = 3610. 19 - 19 = 0

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

square root 1

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

square root 2