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

1 Answer
May 13, 2016

Answer:

#-1/2(sqrt3+sqrt5)#

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)#