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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