Question

Find the square root of 625 using repeated subtraction.

Answer 1

Hint: Here, we will use the method of repeated subtraction i.e., subtracting successive odd numbers from the square till the difference is 0 to find the square root.

Complete step-by-step answer:
We need to find the square root of 625 using the concept of repeated subtraction.
So we will be subtracting odd numbers consequently to reach till zero and the total steps involved to reach zero will be the answer.

$
  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 \\
 $

Now if we count the total number of steps involved to reach 0, it is 25.
Hence the square root of 625 is 25.

Note: In the repeated subtraction method always subtract the number (2n+1) where n=0, 1, 2………. from the result of the previous step starting from n=0, coming till the point we obtain 0 as the final answer, the total number of steps involved till this is the square root. Students should avoid subtraction from even numbers.