Question

Find the square roots of 100 and 169 with the method of repeated subtraction.
Please tell the solution also.

Thanks​

Answer 1

Answer:

00 - 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.

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

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.

we will be using consecutive odd numbers  

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

Thus, we have subtracted consecutive odd numbers from 100 starting from 1. 0 is obtained in the 10th step. So we have √100 = 10

Try for 169 on your own. I am sure you will make it. Go ahead!!