How do you rationalize the denominator and simplify #1/(sqrt3-sqrt5)#?

1 Answer
Noah G
Sep 11, 2016

The expression can be simplified to #-(sqrt(3) + sqrt(5))/2#.

Explanation:

Multiply the entire expression by the conjugate of the denominator. The conjugate can be found by switching the middle sign in the denominator (when the denominator is a binomial , of course).

#=>1/(sqrt(3) - sqrt(5)) xx (sqrt(3) + sqrt(5))/(sqrt(3) + sqrt(5))#

#=>(sqrt(3) + sqrt(5))/(sqrt(9) - sqrt(25))#

#=>(sqrt(3) + sqrt(5))/(3 - 5)#

#=>(sqrt(3) + sqrt(5))/(-2)#

#=> -(sqrt(3) + sqrt(5))/2#

Hopefully this helps!

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