Question

How do you rationalize the denominator and simplify `sqrt3/(2+sqrt2)`?

Answer 1

You multiply by `1`, disguised as `(2-sqrt2)/(2-sqrt2)`

Explanation:

`=(sqrt3xx(2-sqrt2))/((2+sqrt2)xx(2-sqrt2))`

The denominator is now a special product of the sort:
`(A+B)(A-B)=A^2-B^2`

`=(sqrt3xx(2-sqrt2))/(2^2-sqrt2^2)=(2sqrt3-sqrt2*sqrt3)/(4-2)`

`=(2sqrt3-sqrt6)/2=sqrt3-1/2sqrt6`