How do you rationalize the denominator and simplify $1/(1+sqrt(3)-sqrt(5))$ ?

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Answer 1 · 2016-03-30T15:42:00

$(7+3sqrt3+sqrt5+2sqrt15)/11$ = 2.0162, nearly.

Multiply numerator and denominator by $(1+sqrt3+sqrt5)$ .
Use $(a+b)(a-b)=(a^2-b^2)$ for the denominator.

The denominator now is $(1+sqrt3)^2-(sqrt5)^2= 2sqrt3+1$ .

Multiply the numerator and denominator by the conjugate $2sqrt3+1$ of the denominator.

Now, the denominator is rationalized to 11.

Expand the product in the numerator and simplify for the answer.

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How do you rationalize the denominator and simplify 1/(1+sqrt(3)-sqrt(5))1/(1+sqrt(3)-sqrt(5))?