Question

Find the square root of 361 and 625 by using repeated subtraction method.
[5 marks]

Answer 1

Let us find the square root of 361 first.
361 - 1 = 360
360 - 3 = 357
357 - 5 = 352
352 - 7 = 345
345 - 9 = 336
336 - 11 = 325
325 - 13 = 312
312 - 15 = 297
297 - 17 = 280
280 - 19 = 261
261 - 21 = 240
240 - 23 = 217
217 - 25 = 192
192 - 27 = 165
165 - 29 = 136
136 - 31 = 105
105 - 33 = 72
72 - 35 = 37
37 - 37 = 0
Here we performed repeated subtraction 19 times.
Therefore, <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\sqrt{361}$ = 19
[2.5 marks]

Now, let's find the square root of 625.
625 - 1 = 624
624 - 3 = 621
621 - 5 = 616
616 - 7 = 609
609 - 9 = 600
600 - 11 = 589
589 - 13 = 576
576 - 15 = 561
561 - 17 = 544
544 - 19 = 525
525 - 21 = 504
504 - 23 = 481
481 - 25 = 456
456 - 27 = 429
429 - 29 = 400
400 - 31 = 369
369 - 33 = 336
336 - 35 = 301
301 - 37 = 264
264 - 39 = 225
225 - 41 = 184
184 - 43 = 141
141 - 45 = 96
96 - 47 = 49
49 - 49 = 0
Here we performed repeated subtraction 25 times.
Therefore, $\sqrt{625}$ = 25
[2.5 marks]