Question

How do you simplify `(9+3sqrt6) /sqrt3`?

Answer 1

`3sqrt3+3sqrt2`

Explanation:

To simplify `(9+3sqrt6)/sqrt3`, we have to first rationalize denominator. Here as denominator is pure irrational number `sqrt3`, we multiply numerator and denominator both by `sqrt3`.

The fraction than becomes

`((9+3sqrt6)/sqrt3)*sqrt3/sqrt3` or

`(9sqrt3+3sqrt6*sqrt3)/(sqrt3*sqrt3)`, which simplifies to

`(9sqrt3+3sqrt18)/3` or `(9sqrt3+3*3sqrt2)/3` or

`3sqrt3+3sqrt2`