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

1 Answer
Nov 28, 2014

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 .