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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.

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.

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