1. ## Perfect Squares

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?

2. ## re: Perfect Squares

Originally Posted by corihawke
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 $\displaystyle a^2$, where $\displaystyle a$ is an integer.

$\displaystyle 3^6 = \left(3^3\right)^2$ and $\displaystyle 13^2$ are perfect squares, but $\displaystyle 2^3 = \left(2^{\frac{3}{2}}\right)^2$ is not.

3. ## re: Perfect Squares

a perfect square is an integer times itself

$3*3=9=3^2$

4. ## Re: Perfect Squares

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