Question

Without doing calculation, find the numbers which are surely not perfect squares.
(i) $153$
(ii) $257$
(iii) $408$
(iv) $441$

Answer 1

For any number to be perfect square,

It should have a number from $\{1,4,9,6,5\}$ at their units place.

Here,

(i) $153$ ending with $3$, so it cannot be a perfect square.

(ii) $257$ ending with $7$, so it cannot be a perfect square.

(iii) $408$ ending with $8$, so it cannot be a perfect square.

(iv) $441$ ending with $1$, so it can be a perfect square.