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

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Answer 1 · 2018-04-18T08:37:38

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

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

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

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

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

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