Question

How do you simplify `sqrt5/(5+sqrt2)`?

Answer 1

See below.

Explanation:

To simplify, we have to multiply by the conjugate of the denominator, or `5-sqrt2`.

`sqrt5/(5+sqrt2)\cdot(5-sqrt2)/(5-sqrt2)=(5sqrt5-sqrt10)/(25-2)=(5sqrt5-sqrt10)/(23)`