Question

Using repeated subtraction, state whether $125$ is a perfect square or not.

Answer 1

The given number is $125$.

Now, by repeated subtraction,

$125-1=124$

$124-3=121$

$121-5=116$

$116-7=109$

$109-9=100$

$100-11=89$

$89-13=76$

$76-15=61$

$61-17=44$

$44-19=25$

$25-21=4$

$4-23=-19$

Here, by repeated subtraction, we do not get the answer as zero at any point.

Hence, $125$ is not a prefect square.