Question

How do you rationalize the denominator and simplify `(sqrt3+7)/(8-sqrt5)`?

Answer 1

`=(56+sqrt15+7sqrt5+8sqrt3)/59`

Explanation:

To rationalize the denominator, multiply by its reciprocal, which in this case is `8+sqrt5`. To use this operation you must apply it to both the top and the bottom:
`=(sqrt3+7)/(8-sqrt5)*(8+sqrt5)/(8-sqrt5)`
FOIL the top and bottom:
`=(8sqrt3+sqrt15+56+7sqrt5)/(64-8sqrt5+8sqrt5-5)`
Combine all like terms:
`=(56+sqrt15+7sqrt5+8sqrt3)/59`
This is the simplest form.