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

1 Answer
May 1, 2018

Answer:

#=(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.