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))#

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