How do you simplify $(sqrt 3 -sqrt 6) / (sqrt 3 +sqrt6)$ ?

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Answer 1 · 2016-02-10T20:19:47

$=-3+2sqrt(2)$

When you have a sum of two square roots, the trick is to multiply by the equivalent subtraction:

$(sqrt(3)-sqrt(6))/(sqrt(3)+sqrt(6))$

$=(sqrt(3)-sqrt(6))/(sqrt(3)+sqrt(6))*(sqrt(3)-sqrt(6))/(sqrt(3)-sqrt(6))=$

$=((sqrt(3))^2-2*sqrt(3)*sqrt(6)+(sqrt(6))^2)/((sqrt(3))^2-(sqrt(6))^2$

$=(3-2sqrt(18)+6)/(3-6)$

$=(9-2*sqrt(9*2))/-3$

$=(9-2*3sqrt(2))/-3$

$=-3+2sqrt(2)$

How do you simplify (sqrt 3 -sqrt 6) / (sqrt 3 +sqrt6)(sqrt 3 -sqrt 6) / (sqrt 3 +sqrt6)?