Question

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

Answer 1

note: This question comes originally from this page.

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

`3` is equivalent to `sqrt(9)`. Thus,

1.) `1/(3sqrt(1-x^2/9))`

is equivalent to

2.) `1/(sqrt(9)*sqrt(1-x^2/9))`.

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

`sqrt(A)*sqrt(B) = sqrt(A*B)`

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

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

2.) `1/(sqrt(9)*sqrt(1-x^2/9))`

will become:

3.) `1/(sqrt(9(1-x^2/9)))`

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 .