Question

the following number are obviously not perfect square give reason. I. 1057. ii 23453

Answer 1

(1) , (2),don’t have any of the 0, 1, 4, 5, 6, or 9 at unit’s place, so they are not be perfect squares.

Answer 2

It is true that these number are obviously not perfect square :
1057, 23453 .
This is because, see, the last digit of the number determines what the number is a perfect square or not. I will explain my answer. See, we just need to memorise the last digit of the square of all the 1 digit number. See, the list of the last digit of the square of all the 1 digit number is as follows:
1 the last digit of the square of 1 is 1 (1).
2 the last digit of the square of 2 is 4 (4).
3 the last digit of the square of 3 is 9 (9).
4 the last digit of the square of 4 is 6 (16).
5 the last digit of the square of 5 is 5 (25) .
6 the last digit of the square of 6 is 6 (36).
7 the last digit of the square of 7 is 9 (49).
8 the last digit of the square of 8 is 4 (64).
9 the last digit of the square of 9 is 1 (81).

So, if we make any perfect square, the last digit of the number should be 1 of these numbers : 1,4,5,6 or 9 ( as we can see from the above chart ). But, as we can see that the numbers : 1057 and 23453 don't have there last digit as the above mentioned numbers, therefore they are obviously not perfect square ( 7 and 3 are not present in the list ).


Hope this helped you.
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Thanks.