Question

How do you rationalize the denominator `8/(3+sqrt5)`?

Answer 1

Multiply numerator (top) and denominator (bottom) by the conjugate
`3-sqrt(5)` ...

`8/(3+sqrt(5)) = (8(3-sqrt(5)))/((3+sqrt(5))(3-sqrt(5)))`

`=(24-8sqrt(5))/(3^2-sqrt(5)^2)`

`=(24-8sqrt(5))/4`

`=6-2sqrt(5)`