How do you rationalize the denominator and simplify 3/(sqrt5+sqrt6)3√5+√6?

1 Answer
Dean R.
Apr 18, 2018

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

Explanation:

frac {3} {sqrt{5} + sqrt{6} } 3√5+√6

= frac {3} {sqrt{5} + sqrt{6} } cdot \frac{ sqrt{5} - sqrt{6} }{ sqrt{5} - sqrt{6} } =3√5+√6⋅√5−√6√5−√6

= frac { 3 sqrt{5} - 3 sqrt{6} } { 5 - 6 }=3√5−3√65−6

= 3 sqrt{6} - 3 sqrt{5} =3√6−3√5

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