find the square roots of 100 and 169 by the method of repeated subtraction
Answers
Square root by repeated subtraction:
This is the simplest method of finding the square
root of a perfect square. It works very well for small numbers.
Take the number n whose square root is required .
Subtract from and the odd numbers 1, 3, 5 7, 9….. successively . If n is a
perfect square we will get zero at some stage . We stop at this point and
declared the number of times we have perform subtraction as the square root of
n.
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Solution:
√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
9. 36-17=19
10. 19 - 19 = 0
We get 0 at 10th step. Hence,10 is the square root of 100.
√100 = 10
√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. Hence,13 is the square root of 169
√169=13
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Hope this will help you.....
Explanation:
100-1= 99
99-3=96
96-5=91
91-7=84
84-9=75
75-11=64
64-13=51
51-15=36
36-17=19
19-19=0
there for 100 is subtracted 10 times so the square root of 100 is 10