why isnt 2(with a 3 above it) x 3(with a 6 above it) x 13(with a 2 above it) not a perfect square number?
also,can anyone explain a square number?
A perfect square can be written as $\displaystyle \displaystyle a^2$, where $\displaystyle \displaystyle a$ is an integer.
$\displaystyle \displaystyle 3^6 = \left(3^3\right)^2$ and $\displaystyle \displaystyle 13^2$ are perfect squares, but $\displaystyle \displaystyle 2^3 = \left(2^{\frac{3}{2}}\right)^2$ is not.
remember that anything raised to a power can be written as the number raised to a factor of that power, and then raised to the other factor:
3^6 = (3^3)^2
So anything raised to an EVEN power is a perfect square.
If you have several factors, each raised to an even power, they can all be rewritten as a perfect square. Remember:
(a^2)(b^2) = (a*b)^2
So if all 3 of your factors can be written like this, the whole thing can be written as a perfect square. But one of the numbers you gave was raised to an ODD power, meaning it can't be rewritten as a perfect square.
Aaron McDevitt