How do you rationalize the denominator?

1 Answer
Dec 23, 2014

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)#