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Question:

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

Solution:

For any number to be a perfect square, it should have a number from 1, 4, 9, 6, 5 at its 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.