Find the sum of the proper divisors of that number.
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You can tell whether a number is a square number by looking at the last digit. A perfect square number ends with either 1, 4, 5, 6, 9 or 00.
A trinomial is perfect square if it can be factored into the form
One way is to get the prime factorization of the number. If every prime occurs an even number of times, it is a square, otherwise, not. Another is to estimate the square root of the number, and square it. If you get more than the number, try a lower estimate; if less, a higher one. Using interval bisection you very quickly zero in on the square root, if it is a whole number. If so, the number is a perfect square. Otherwise, you find 2 consecutive whole numbers between which is the square root, in which case it is not a perfect square.
It is not easy. If the value is rational then you must be able to express the value under the radical sign as p2/q2 where p and q are integers and q is non-zero. If not, then the number is irrational.It is not enough to require that for a rational, the number under the radical must be a perfect square since sqrt(2.25) is rational even though 2.25 is not a perfect square.
16 is a perfect square because you can arrange exactly 16 balls or matches or circles in a square with equal sides. Refer to the diagram below.* * * ** * * ** * * ** * * *See the sides. There are exactly 4 stars on each of the sides. 4 x 4 = 16. That is how you can tell if something is a square number. 1 x 1 = 1. 2 x 2 = 4 and so on. Any number which you can arrange into a perfect square is a square number. That is why they are called square numbers int eh first place.