Question

How do you rationalize the denominator and simplify `[2sqrt(5) - 3sqrt(2)] / [2sqrt(5) + 3sqrt(2)]`?

Answer 1

`19 - 3sqrt10`

Explanation:

Multiply both numerator and denominator by `(2sqrt5 - 3sqrt2)`

`[(2sqrt5- 3sqrt2)/(2sqrt5 + 3sqrt2)][(2sqrt5 - 3sqrt2)/(2sqrt5 - 3sqrt2)] =(2sqrt5 - 3sqrt2)^2/(20 - 18) = (20 + 18 - 6sqrt10)/2 =`
`= 19 - 3sqrt10`