How do you rationalise the denominator of 8/(3-sqrt5)?

1 Answer
George C.
Apr 3, 2016

Multiply both numerator and denominator by 3+sqrt(5) and simplify.

Explanation:

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))/(9-5)

=(24+8sqrt(5))/4

=6+2sqrt(5)

The expression (3+sqrt(5)) is called the conjugate of (3-sqrt(5))

Related questions
See all questions in Fractions with Different Denominators
Impact of this question
3548 views around the world
You can reuse this answer
Creative Commons License