How do you rationalize the denominator and simplify 5/(sqrt3+sqrt5)5√3+√5?

1 Answer
Gió
Jan 18, 2017

I got as far as: -5/2*(sqrt(3)-sqrt(5))−52⋅(√3−√5)

Explanation:

You can multiply and divide by sqrt(3)-sqrt(5)√3−√5 and take advantage of the fact that: (a+b)(a-b)=a^2-b^2(a+b)(a−b)=a2−b2 and write:

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

=(5*(sqrt(3)-sqrt(5)))/(3-5)=-5/2*(sqrt(3)-sqrt(5))=5⋅(√3−√5)3−5=−52⋅(√3−√5)

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