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

1 Answer
MAXIMILIAN C.
May 1, 2018

=(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.

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1664 views around the world
You can reuse this answer
Creative Commons License