Question

find the square roots of 100 and 169 by the method of repeated subtraction. ​​

Answer 1

√100 by Repeated subtraction:

100 - 1 = 99. 99 - 3 = 96. 96 - 5 = 91. 91 -7 = 84. 84 - 9 = 75. ...

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

√100 = 10.

√169 by Repeated subtraction:

169 - 1 = 168. 168 - 3 = 165. 165 - 5 = 160. 160 - 7 = 153. 153 - 9 = 144. ...

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

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Answer 2

Answer:

For square root we'll subtract successive odd numbers till we obtain zero. Then, the total numbers we subtract is the square root of that number.

a.) 100

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
9. 36 - 17 = 19
10. 19 - 19 = 0

Here, we got 0 after subtracting 10 odd numbers.

Therefore, square root of 100 is 10.

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b.) 169

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

Here, we got 0 after subtracting 13 odd numbers.

Therefore, square root of 169 is 13.