How do you rationalise the denominator of 8/(3-sqrt5)83−√5?

1 Answer
George C.
Apr 3, 2016

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

Explanation:

8/(3-sqrt(5))83−√5

=(8*(3+sqrt(5)))/((3-sqrt(5))(3+sqrt(5)))=8⋅(3+√5)(3−√5)(3+√5)

=(24+8sqrt(5))/(3^2-(sqrt(5))^2)=24+8√532−(√5)2

=(24+8sqrt(5))/(9-5)=24+8√59−5

=(24+8sqrt(5))/4=24+8√54

=6+2sqrt(5)=6+2√5

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

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