Question

How do you simplify `(2sqrt3+sqrt2)/(sqrt3+2sqrt2)`?

Answer 1

Multiply both numerator (top) and denominator (bottom) by the conjugate (see example) of the denominator.

`(2sqrt(3)+sqrt(2))/(sqrt(3)+2sqrt(2))*(sqrt(3)-2sqrt(2))/(sqrt(3)-2sqrt(2))`

`= (2(3) +sqrt(2)sqrt(3)-4sqrt(2)sqrt(3)-2(2))/(3-8)`

`=(10 - 3sqrt(6))/(-5)`

`= 3/5sqrt(6) -2`