How do you rationalize the denominator and simplify 3/(4+4sqrt5)?

1 Answer
George C.
Sep 26, 2015

Multiply both numerator and denominator by (sqrt(5)-1) and rearrange to find:

3/(4+4sqrt(5)) =(3sqrt(5)-3)/16

Explanation:

Using the identity a^2-b^2 = (a-b)(a+b) we find:

3/(4+4sqrt(5))

=3/(4(1+sqrt(5))

=3/(4(sqrt(5)+1)

=3/(4(sqrt(5)+1))*((sqrt(5)-1))/((sqrt(5)-1))

=(3(sqrt(5)-1))/(4(sqrt(5)-1)(sqrt(5)+1))

=(3(sqrt(5)-1))/(4((sqrt(5))^2-1^2))

=(3(sqrt(5)-1))/(4(5-1))

=(3(sqrt(5)-1))/16

=(3sqrt(5)-3)/16

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