**Quote:**

But how does 4 / √3 turn into 4√3 / 3? Isn't that an extra three?

This is the method to eliminate radicals in a denominator.

We multiply the numerator and denominator by the same number, √3.

4 / √3 = 4√3 / (√3 × √3)

The denominator, √3 × √3, results in (√3)² = 3 . So we get:

4 / √3 = (4√3) / 3

**Quote:**

I always seem to mess them up and the only thing I ever read is telling me to group radicals together and treat regular numbers separately.

If you are Ok with exponents, then you can treat radicals as exponents.

√

*a* is

*a* to the (1/2)th power

Another two simple ideas that should get you started on roots are:

1. √

*a* × √

*a* =

*a*³√

*a* × ³√

*a* × ³√

*a* =

*a* 2. Roots are Ok to multiply in & out (as long as all the numbers under the sign are non-negative):

√(2/3) = √2 / √3

√6 = √(2 × 3) = √2 × √3

√6 / √2 = √(6/2) = √3

or

√6 / √2 = √3 × √2 / √2 = √3

If you get the feeling of these two basic concepts, that should allow you to move on to dealing with addition. For example we can transform: √6 + √2 = √2 (√3 + 1).