# How do you simplify # (5-3sqrt6)/(3+4sqrt2)#?

##### 2 Answers

#### Explanation:

In order to rationalize the denominator, we multiply it by its conjugate (the conjugate of

The conjugate of the denominator

Since we are going to multiply its denominator by

Then, we have

We can simplify the denominator by using the identity

#### Explanation:

We can simplify the denominator by turning it into a single term by multiplying the fraction by the conjugate of the denominator.

The conjugate of

So, we multiply the numerator and denominator by

#(5-3sqrt6)/(3+4sqrt2)*(3-4sqrt2)/(3-4sqrt2)=((5-3sqrt6)(3-4sqrt2))/((3+4sqrt2)(3-4sqrt2))#

Expand both of these by FOILing:

#=(15-(3sqrt6)3+5(-4sqrt2)-3sqrt6(-4sqrt2))/(9+(4sqrt2)3+3(-4sqrt2)+(4sqrt2)(-4sqrt2))#

Simplifying these:

#=(15-9sqrt6-20sqrt2+12sqrt12)/(9+12sqrt2-12sqrt2-16sqrt4)#

Note that

#=(15-9sqrt6-20sqrt2+12(2sqrt3))/(9-16(2))#

#=(15-9sqrt6-20sqrt2+24sqrt3)/(9-32)#

#=(15-9sqrt6-20sqrt2+24sqrt3)/(-23)#