Please go through the article on perfect square numbers if you want better understanding on what are perfect square numbers.

If you are given a list of numbers, can we rule out numbers from the list which are definitely not perfect square numbers. Certainly, we can.

Lets write some perfect square numbers here.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361 and 400.

Note that perfect square numbers always end with 0, 1, 4, 5, 6 or 9. Choose any perfect square number and you will find that it is ending with 0, 1, 4, 5, 6 or 9. Find the squares of numbers using the property and you will find that all of them are ending with 0, 1, 4, 5, 6 or 9.

**So it means that all the non-perfect square numbers end with 2, 3, 7 or 8.**

**Please note that all the perfect square numbers end with 0, 1, 4, 5, 6 or 9 but all the numbers with end with 0, 1, 4, 5, 6 or 9 are not perfect square numbers. Example, 11, 21, 51, 79, 76 etc. are the numbers which are not perfect square numbers.**

I have a list for you now.

2282, 5783, 2116, 5929, 62411, 729788. Can you rule out those numbers from the list which cannot be perfect square numbers by just looking at them?

5783 ends with 3, 2282 ends with 2, 729788 ends with 8. By just looking at these 3 numbers, we can rule out them from the list and can say that they are definitely not the perfect square numbers. We cannot say that the rest of the numbers are perfect square numbers just because they end with 0, 1, 4, 5, 6 or 9. Example 62411 ends with 1 but it is not a perfect square number.

Which of them is a perfect square number?

(A) 458782

(B) 451288

(C) 45857

(D) 952323

(E) None of these

458782 ends with 2, 451288 ends with 8, 45857 ends with 7 and 952323 ends with 3. Therefore, all of them are non-perfect square numbers. Hence, the answer is (E).