Question

Which of the following numbers has the possibility of having perfect squares:
(1) 9285
(2) 2312
(3) 2307
(4) 2001
(5) 2305
(6) 2508
(7) 2160
(8) 44101
(9) 1069

Answer 1

First of all let me tell which numbers are called as perfect squares. Not all squares are called as perfect squares, the square of integers only are called as perfect squares.

Now we have 10 distinct digits in maths. They are 0,1,2,3,4,5,6,7,8,9

I assume all of us know the square of this numbers. From that concept there is a probability that numbers ending with 1, 4, 5, 6, 9 or 00 will be a perfect square.

We can also predict that the numbers ending with 2, 3, 7 or 8 is not a perfect square.

Therefore, numbers that has the possibility of having perfect squares are:

(1) 9285

(4) 2001

(5) 2305

(8) 44101

(9) 1069

Now there are some more steps which are a bit complex using which we can excatly find out which are the perfect square numbers.