# How can you simplify 1/(3sqrt(1-x^2/9))?

Nov 28, 2014

To simplify this expression I brought the $3$ "inside" the radical.

$3$ is equivalent to $\sqrt{9}$. Thus,

1.) $\frac{1}{3 \sqrt{1 - {x}^{2} / 9}}$

is equivalent to

2.) $\frac{1}{\sqrt{9} \cdot \sqrt{1 - {x}^{2} / 9}}$.

A common law of radicals is the law of "combining," which basically looks like:

$\sqrt{A} \cdot \sqrt{B} = \sqrt{A \cdot B}$

where $A$ and $B$ can be anything.

Using this law we can simplify our expression a little further.

2.) $\frac{1}{\sqrt{9} \cdot \sqrt{1 - {x}^{2} / 9}}$

will become:

3.) $\frac{1}{\sqrt{9 \left(1 - {x}^{2} / 9\right)}}$

Now, all that's left is to distribute the $9$. This gives us:

4.) 1/(sqrt(9 - x^2)

which looks a lot less ugly than what we started with in 1 .