Question

Find the square root of $121$ using repeated subtraction.

Answer 1

Hint: Repeated subtraction is a method of subtracting the equal number of items from a larger group. It is also known as division. If the same number is repeatedly subtracted from another larger number until the remainder is zero or a number smaller than the number being subtracted, we can write that in the form of division. The square root of $121$ is the number which multiplied by itself will give $121$.

We are going to start subtracting the number $121$ with $1$ and then move on with the next odd number $3$ and so on,
Therefore,
$121 - 1 = 120$
Next odd number is $3$, we are going to take the resultant number from above step and subtract $3$,
Therefore,
$120 - 3 = 117$
Similarly,
$117 - 5 = 112$
$112 - 7 = 105$
$105 - 9 = 96$
$96 - 11 = 85$
$85 - 13 = 72$
$72 - 15 = 57$
$57 - 17 = 40$
$40 - 19 = 21$
$21 - 21 = 0$
As soon as we get zero, we stop the process and count the number of times the subtraction has taken place, in this case it is $11$.

Note: Make sure you count the number of steps correctly, because that is going to be the answer.
Therefore, $11$ is the square root of $121$.