## anonymous one year ago Step by step instruction?

1. anonymous

$\frac{ \sqrt{6} }{ \sqrt{5}-\sqrt{3} }$

2. anonymous

Rationalize the denominator and simplify.

3. Vocaloid

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

4. Vocaloid

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

5. anonymous

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.

6. Vocaloid

actually, yeah, that's right

7. Vocaloid

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

8. Vocaloid

but other than that you've got the answer

9. anonymous

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

10. Vocaloid

$\sqrt{18}=\sqrt{9*2}=\sqrt{3*3*2}=3\sqrt{2}$

11. anonymous

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

12. Vocaloid

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

13. Vocaloid

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

14. Vocaloid

so your final answer would be $\frac{ \sqrt{30}-3\sqrt{2} }{ 2 }$

15. anonymous

Ok yeah I think I get it thank you.

16. Vocaloid