Question

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

Answer 1

We need to find square root of $121$ by repeated subtraction method.

$121-1=120$

$120-3=117$

$117-5=112$

$112-7=105$

$105-9=96$

$96-11=85$

$85-13=72$

$72-15=57$

$57-17=40$

$40-19=21$

$21-21=0$

We have subtract odd numbers from the given number.

So, we start with subtracting $1$ form $121$ which gives us $120$.

Now, subtract $3$ from $120$ which is $117$.

The process 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.

In this case, we had to subtract in $11$ steps to get to $0$. Hence, root of $121$ is $11$.