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

Answer

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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 $121$.

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 $121$.

Last updated date: 24th Sep 2023

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