# How do you rationalize the denominator and simplify #1/ (sqrt 3 - sqrt 5)#?

##### 1 Answer

May 13, 2016

#### Explanation:

What we have to do here is to multiply the numerator and denominator by the

#color(blue)" conjugate"" of the denominator"# The conjugate here is

#sqrt3+sqrt5# Note that the radicals remain unchanged ,while the 'sign' changes.

If

#sqrt3-sqrt5" then conjugate" =sqrt3+sqrt5#

#rArr1/(sqrt3-sqrt5)=(1(sqrt3+sqrt5))/((sqrt3-sqrt5)(sqrt3+sqrt5))#

Consider the denominator.

#(sqrt3-sqrt5)(sqrt3+sqrt5)" and expand using FOIL"#

#=(sqrt3)^2+cancel(sqrt5 .sqrt3)-cancel(sqrt5 .sqrt3)-(sqrt5)^2#

#=3-5=-2" which is rational"#

#rArr1/(sqrt3-sqrt5)=(sqrt3+sqrt5)/(-2)=-1/2(sqrt3+sqrt5)#