Question

How do you rationalize the denominator?

Answer 1

When you have a root (square root for example) in the denominator of a fraction you can "remove" it multiplying and dividing the fraction for the same quantity. The idea is to avoid an irrational number in the denominator.
Consider:
`3/sqrt2`
you can remove the square root multiplying and dividing by `sqrt2`;
`3/sqrt2*sqrt2/sqrt2`
This operation does not change the value of your fraction because `sqrt2/sqrt2=1` anyway and your fraction does not change by multiplying `1` to it.

Now you can multiply in the numerator and denominator:
`3/sqrt2*sqrt2/sqrt2=(3*sqrt2)/((sqrt2)*(sqrt2))` giving:
`(3*sqrt2)/2` you have removed the square root from the denominator! (ok it went to the nominator but this is ok).

Now a problem for you; what happens when the root is not alone???!!!
If you have:
`3/(1+sqrt2)`???
You can use the same technique but...what do you use to multiply and divide?
HINT: look at what happens if you do this:
`(1+sqrt2)*(1-sqrt2)`