Question

How do you simplify `5/(4 + sqrt5)`?

Answer 1

See a solution process below:

Explanation:

To simplify this express we need to rationalize the denominator. Or, in other words, remove the radicals from the denominator. We can do this by multiplying by the appropriate form of `1`:

`(4 - sqrt(5))/(4 - sqrt(5)) xx 5/(4 + sqrt(5)) => (5(4 - sqrt(5)))/(4^2 + 4sqrt(5) - 4sqrt(5) + (sqrt(5))^2) =>`

`((5 xx 4) - (5 xx sqrt(5)))/(16 + (4sqrt(5) - 4sqrt(5)) + 5) =>`

`(20 - 5sqrt(5))/(16 + 0 + 5) =>`

`(20 - 5sqrt(5))/21`

Or

`20/21 - (5sqrt(5))/21`