How do you rationalize the denominator and simplify #3/(sqrt5+sqrt6)#?

1 Answer
Dean R.
Apr 18, 2018

We multiply by # \frac{ sqrt{5} - sqrt{6} }{ sqrt{5} - sqrt{6} } # to rationalize the denominator.

Explanation:

# frac {3} {sqrt{5} + sqrt{6} } #

# = frac {3} {sqrt{5} + sqrt{6} } cdot \frac{ sqrt{5} - sqrt{6} }{ sqrt{5} - sqrt{6} } #

# = frac { 3 sqrt{5} - 3 sqrt{6} } { 5 - 6 }#

# = 3 sqrt{6} - 3 sqrt{5} #

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