Question

Find the square root of the following numbers by the repeated subtraction method.
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Answer 1

Answer:

We know that the sum of the first n odd natural numbers is n2. We will use this fact to find square root of a number by repeated subtraction. Let us take an example to learn this method. Say, you are required to find the square root of 121, that is, √121. The steps are:

1. 121 – 1 = 120
2. 120 – 3 = 117
3. 117 – 5 = 112
4. 112 – 7 = 105
5. 105 – 9 = 96
6. 96 – 11 = 85
7. 85 – 13 = 72
8. 72 – 15 = 57
9. 57 – 17 = 40
10. 40 – 19 = 21
11. 21 – 21 = 0

Thus, we have subtracted consecutive odd numbers from 121 starting from 1. 0 is obtained in the 11th step. So we have √121 = 11.