Question

Step by step instruction?

Answer 1

\[\frac{ \sqrt{6} }{ \sqrt{5}-\sqrt{3} }\]

Answer 2

Rationalize the denominator and simplify.

Answer 3

the conjugate of the denominator is sqrt(5)+sqrt(3) (change the sign in the middle)
\[\frac{ \sqrt{6} }{ \sqrt{5}-\sqrt{3}} * \frac{ \sqrt{5}+\sqrt{3} }{ \sqrt{5}+\sqrt{3}} \]

Answer 4

multiply all of that out and simplify. there should be no radicals left in the denominator when you're done

Answer 5

Ok well I think I'm left with \[\frac{ \sqrt{30}+\sqrt{18} }{ 2 }\] but I'm not sure if I did the math right.

Answer 6

actually, yeah, that's right

Answer 7

just know that you can simplify \[\sqrt{18} = 3\sqrt{2}\]

Answer 8

but other than that you've got the answer

Answer 9

Ok I'm not really sure how to simplify \[\sqrt{18}\] to get \[3\sqrt{2}\] is there a process to get there?

Answer 10

\[\sqrt{18}=\sqrt{9*2}=\sqrt{3*3*2}=3\sqrt{2}\]

Answer 11

So how would I do that to the \[\sqrt{30}\] or can't I? would it look like this: \[\sqrt{5*3*2}\]

Answer 12

you can't, the square root of 30 is already simplified

Answer 13

we can simplify the square root of 18 because it contains a perfect square (9) as a factor

you can write square root of 30, no need to do anything else to it

Answer 14

so your final answer would be

\[\frac{ \sqrt{30}-3\sqrt{2} }{ 2 }\]

Answer 15

Ok yeah I think I get it thank you.

Answer 16

*small correction, there should be a plus sign in the numerator