How do you rationalize the denominator and simplify 1 / (sqrt5+sqrt6)?

1 Answer
George C.
Mar 16, 2016

1/(sqrt(5)+sqrt(6)) = sqrt(6)-sqrt(5)

Explanation:

It works out a little easier if you swap sqrt(5)+sqrt(6) around first.

Multiply both numerator and denominator by the conjugate sqrt(6)-sqrt(5) of the denominator:

1/(sqrt(5)+sqrt(6))

=1/(sqrt(6)+sqrt(5))

=(sqrt(6)-sqrt(5))/((sqrt(6)-sqrt(5))(sqrt(6)+sqrt(5)))

=(sqrt(6)-sqrt(5))/((sqrt(6))^2-(sqrt(5))^2)

=(sqrt(6)-sqrt(5))/(6-5)

=(sqrt(6)-sqrt(5))/1

=sqrt(6)-sqrt(5)

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