Question

find the square root by the repeated subtraction. 144 and 676
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Answer 1

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Answer 2

Question :- find the square root by the repeated subtraction :- 144 and 676 ?

Concept :-

• we have subtracted consecutive odd numbers from 1 till we get 0.

Solution :-

Square root of 144 :-

1. 144 - 1 = 143
2. 143 - 3 = 140
3. 140 - 5 = 135
4. 135 - 7 = 128
5. 128 - 9 = 119
6. 119 - 11 = 108
7. 108 - 13 = 95
8. 95 - 15 = 80
9. 80 - 17 = 63
10. 63 - 19 = 44
11. 44 - 21 = 23
12. 23 - 23 = 0 .

Therefore, we have subtracted consecutive odd numbers from 144 starting from 1. 0 is obtained in the 12th step.

Hence, Square root of 144 is 12.

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Square root of 676 :-

1. 676 - 1 = 675
2. 675 - 3 = 672
3. 672 - 5 = 667
4. 667 - 7 = 660
5. 660 - 9 = 651
6. 651 - 11 = 640
7. 640 - 13 = 627
8. 627 - 15 = 612
9. 612 - 17 = 595
10. 595 - 19 = 576
11. 576 - 21 = 555
12. 555 - 23 = 532 .
13. 532 - 25 = 507
14. 507 - 27 = 480
15. 480 - 29 = 451
16. 451 - 31 = 420
17. 420 - 33 = 387
18. 387 - 35 = 352
19. 352 - 37 = 315
20. 315 - 39 = 276
21. 276 - 41 = 235
22. 235 - 43 = 192
23. 192 - 45 = 147
24. 147 - 47 = 100
25. 100 - 49 = 51
26. 51 - 51 = 0 .

Therefore, we have subtracted consecutive odd numbers from 676 starting from 1. 0 is obtained in the 26th step.

Hence, Square root of 676 is 26.

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