Question

Find the square root of $484$ using repeated subtraction.

Answer 1

We have subtract odd numbers from the given number.

So, we start with subtracting $1$ from $484$ which gives us $483$.

Now, subtract $3$ from $483$ which is $480$.

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.

$484-1=483$

$483-3=480$

$480-5=475$

$468-9=459$

$459-11=448$

$448-13=435$

$435-15=420$

$420-17=403$

$403-19=384$

$384-21=363$

$363-23=340$

$340-25=315$

$315-27=288$

$288-29=259$

$259-31=228$

$228-33=195$

$195-35=160$

$160-37=123$

$123-39=84$

$84-41=43$

$43-43=0$

In this case, we had to subtract in $22$ steps to get to $0$. Hence, root of $484$ is $22$.