Question

Find the square root of $100$ using repeated subtraction.

Answer 1

We need to find square root of $100$ by repeated subtraction method.

It is done as follows:

$100-1=99$

$99-3=96$

$96-5=91$

$91-7=84$

$84-9=75$

$75-11=64$

$64-13=51$

$51-15=36$

$36-17=19$

$19-19=0$

We have subtract odd numbers from the given number.

So, we start with subtracting $1$ form $100$ which gives us $99$.

Now, subtract $3$ from $99$ which is $96$.

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 $10$ steps to get to $0$. Hence, root of $100$ is $10$.