# Given the prime factorization of an integer how can you determine if our integer is a perfect square?

### What is the definition of a non perfect square?

I have never before heard of a non-perfect square but I suppose it would be any non-zero number that is not the square of an integer. People sometimes say "perfect square" to mean an integer that is a square of an integer - I think the "perfect" is redundant but if you do not think "square" is clear by itself, say "integer square."

### Is the product of two perfect squares sometimes a perfect square?

yes..always a perfect square A perfect square is the product of an integer by itself. If you multiply a perfect square x² by another perfect square y² you get x²y² = x·x·y·y = x·y·x·y = (x·y)² which is a perfect square. Note that the product of two integers will also be an integer so x·y must be an integer because if x² and y² are perfect squares x must be an integer and y must…

### What make a number a perfect square number?

A perfect square is the square of an integer, i.e., an integer multiplied by itself. For example, 25 is a perfect square, because 5 x 5 = 25. But, in literal mathematical terms, a perfect number is a positive integer that is the sum of its proper positive divisors, excluding the number itself. A square number is also called a "perfect square", so an example of a square number is above. So, a perfect square…