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

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.

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

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

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

If the units digit of a number is 2, 3, 7 or 8 then it is not a perfect square and hence does not have a square root.

 

If a number has a square root then its units digit must be 0, 1, 4, 5, 6 or 9.

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Solution:

(i)153           (ii) 257           (iii) 408 are not perfect squares

Since, (i), (ii) and (iii) are surely not be perfect square as these numbers end with 3, 7 and 8.

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Hope this will help you....