Question

Without doing any calculation, find the numbers which are surely not perfect squares.

1. 153
2. 257
3. 408
4. 441

Answer 1

The perfect squares of a number can end with any of the digits $0, 1, 4, 5, 6$, or $9$ at unit's place.
Also, a perfect square will end with even number of zeroes, if any.
(i) Since the number $153$ has its unit's place digit as $3$, it is not a perfect square.

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(ii) Since the number $257$ has its unit's place digit as $7$, it is not a perfect square.

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(iii) Since the number $408$ has its unit's place digit as $8$, it is not a perfect square.

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(iv) Since the number $441$ has its unit's place digit as $1$, it is a perfect square.