Why isnt 1953125 a square number

Since the question is why 1953125 is not a square number, you don't need a test for perfect squares, you only need something that shows this particular number is not a perfect square.

One starting test for showing a number will NOT be a perfect square is to use "casting out 9's". Remove any digits that are 9 or that add up to 9.

Thus: 1953125 becomes 153125 (removing 9) which then becomes 125 since 1+5+3=9. [OR: 53, since 1+1+2+5 = 9] [OR: 35]

(Note that you can repeat the whole process until you have cast out all 9s.)

Examine the number that is left. If it is not a perfect square, then the original number cannot be a perfect square.

125 is not a perfect square [nor is 53 or 35], so 1953125 cannot be a perfect square.