Question

# Find the square root of 484 using repeated subtraction.

Hint: To find a square root, we subtract consecutive odd numbers from the given number till we get zero. The number of steps in the process gives the desired result.

We have to subtract odd numbers from the given number.
So, we start with subtracting 1 from 484 which gives us 483.
Now, subtract 3 from 483 which is 480.
The process still continues till we get the final answer as 0.
The number of steps for which this operation has been performed will give the square root of the number.
484 â€“ 1 = 483
483 â€“ 3 = 480
480 â€“ 5 = 475
475 â€“ 7 = 468
468 â€“ 9 = 459
459 â€“ 11 = 448
448 â€“ 13 = 435
435 â€“ 15 = 420
420 â€“ 17 = 403
403 â€“ 19 = 384
384 â€“ 21 = 363
363 â€“ 23 = 340
340 â€“ 25 = 315
315 â€“ 27 = 288
288 â€“ 29 = 259
259 â€“ 31 = 228
228 â€“ 33 = 195
195 â€“ 35 = 160
160 â€“ 37 = 123
123 â€“ 39 = 84
84 â€“ 41 = 43
43 â€“ 43 = 0
In this case we had to subtract 22 times to get zero.
$\therefore$ The root of 484 is 22.

Note:
The number of steps needed to reach zero when we subtract the consecutive odd number will be the square root of the given number. However if the given number is not a perfect square number we will never get zero. So this method effectively defines the square roots of perfect square numbers only.