# What are perfect squares?

A perfect square is a rational number that is the square of another rational number. 9, 16, 25, etc., are perfect squares of 3, 4, 5, etc., and X2 + 6X + 9 is a perfect square of (X + 3).

### What two square numbers total 21?

There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers. There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers. There is no pair of perfect squares that sums to 21…

### How can you two perfect squares for a given integer?

The proposition in the question is simply not true so there can be no answer! For example, if given the integer 6: there are no two perfect squares whose sum is 6, there are no two perfect squares whose difference is 6, there are no two perfect squares whose product is 6, there are no two perfect squares whose quotient is 6.

### Can you write every integer as the sum of two nonzero perfect squares?

No. First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive. Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem No. First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive. Second, for natural numbers (1, 2, 3...) you may need up to 4…

### What is the number of perfect squares that exist in base 5 system?

There are infinitely many, just like in base 10. In any base system, the number of perfect squares is the same. Take the natural (counting) numbers 1, 2, 3, .... Squaring each of these produces the perfect squares. As there are an infinite number of natural numbers, there are an infinite number of perfect squares. The first 10 perfect squares in base 5 are: 15, 45, 145, 315, 1005, 1215, 1445, 2245, 3115, 4005, ...