How do you rationalize the denominator #(3 sqrt 5 + 2) / (3 sqrt 5 + 5)#?

1 Answer
Eric Sandin
Jun 4, 2015

You must look for a binomial that multiplied by the denominator makes the root disappear.

Usually, when you want to rationalize a binomial denominator you will multiply it by its conjugate, in this case #(3sqrt(5)-5)#.
As you know, in order to preserve the fraction, you will multiply it by 1, which is the same as #(3sqrt(5)-5)/(3sqrt(5)-5)#.

#((3sqrt(5)+2))/((3sqrt(5)+5))((3sqrt(5)-5))/((3sqrt(5)-5))=(45-15sqrt(5)+6sqrt(5)-10)/(45-25)=(35-11sqrt(5))/20#

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