Question

rationalize the denominator
sqrt 6/sqrt 3 + sqrt 5

Answer 1

is sqrt 3 + sqrt 5 the denominator?

Answer 2

yes

Answer 3

you should multiple up and down on sqrt 3 - sqrt 5, and use formula (a-b)(a+b) = a^2-b^2

Answer 4

So you will have (sqrt 6)(sqrt 3 - sqrt 5)/(3 - 5)

Answer 5

we do what is called multiplying by the conjugate
the conjugate of a+b is a-b. this is especially useful for imaginary numbers. in your case, as nikita pointed out,
\[\frac{\sqrt{6}}{\sqrt{3}+\sqrt{5}} = \frac{\sqrt{6} \times (\sqrt{3}-\sqrt{5})}{(\sqrt{3}+\sqrt{5})\times (\sqrt{3}-\sqrt{5})} = \frac{\sqrt{6} \times (\sqrt{3}-\sqrt{5})}{3-5}\]

Answer 6

ok thanks you guys are great

Answer 7

you are welcome