Question

How do you simplify `(sqrt5+2sqrt2)/(4-sqrt5)`?

Answer 1

Use the conjugate of the denominator to turn it into a whole number. Details below...

Explanation:

The first thing you want to do is eliminate the radical expression in the denominator. To do this, multiply top and bottom by the conjugate of the denominator, namely `4+sqrt5`

`((sqrt5 + 2sqrt2)(4+sqrt5))/((4-sqrt5)(4+sqrt5))`

Use the FOIL method to multiply top and bottom

`(4sqrt5+5+8sqrt2+2sqrt10)/(16-5)`

`(4sqrt5+5+8sqrt2+2sqrt10)/11`

I think that is all you can do!