Question

Explain with reason whether the given number is perfect square or not: 257

Answer 1

Given number is $257$.

We know that, a number is a perfect square if its square root is a whole number.

Also, every perfect square has one of the following as the digit at its units place:

$1,4,5,6,9$ or even number of $0s$.

It is because:

$1^2=1$

$2^2=4$

$3^2=9$

$4^2=16$

$5^2=25$

$6^2=36$

$7^2=49$

$8^2=64$

$9^2=81$

${10}^2=100$

We see that, $257$ has $7$ at its units place.

Hence, $257$ is not a perfect square.