Question

The no. 257 and 5050 are not perfect squares give reason

Answer 1

257 is not a perfect square as it contains the ones digit as 7 (units/ones digit of numbers containg 2,3,7,8 are never perfect squares).

5050 is not a perfect square as it contains odd number of trailing zerores(1 zero in this case).

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Answer 2

Given: Two numbers 257 and 5050

To find: The reason why 257 and 5050 are not perfect squares

Solution: Using Prime Factorization method, the given numbers can be expressed as:

257 = 257 × 1

5050 = 2 × 5 × 5 × 101 × 1

257 has to be multiplied with 257 so that the resulting product becomes a perfect square and 5050 has to be multiplied with 2 × 101 to get a perfect square.

Now, since 257 and 5050 have unpaired factors in their prime factorization, these numbers are not perfect squares.