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OpenStudy (anonymous):

rationalize the denominator sqrt 6/sqrt 3 + sqrt 5

7 years ago
OpenStudy (anonymous):

is sqrt 3 + sqrt 5 the denominator?

7 years ago
OpenStudy (anonymous):

yes

7 years ago
OpenStudy (nikita2):

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

7 years ago
OpenStudy (nikita2):

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

7 years ago
OpenStudy (anonymous):

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, \[\frac{\sqrt{6}}{\sqrt{3}+\sqrt{5}} = \frac{\sqrt{6} \times (\sqrt{3}-\sqrt{5})}{(\sqrt{3}+\sqrt{5})\times (\sqrt{3}-\sqrt{5})} = \frac{\sqrt{6} \times (\sqrt{3}-\sqrt{5})}{3-5}\]

7 years ago
OpenStudy (anonymous):

ok thanks you guys are great

7 years ago
OpenStudy (anonymous):

you are welcome

7 years ago
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