Quadratic Radicals?

Question

How do I simplify the following (a slash "/" indicates a fraction -- not division):

(sqrt)3/2 + 5(sqrt)6

I understand that the (sqrt)3/2 = (sqrt)6 / 4t =(sqrt)6 / 2.

Now, what do I do with the 5(sqrt)6 AND how do I combine that with (sqrt)6 / 2

Thanks!

Answer 1

if by this you mean

(sqrt(3/2)) + 5sqrt(6)

then as you stated sqrt(3/2) = (sqrt(6))/2

((sqrt(6))/2) + 5sqrt(6)

Multiply everything by 2

(sqrt(6) + 10sqrt(6))/2

((1 + 10)sqrt(6))/2

ANS : (11sqrt(6))/2 or (11/2)sqrt(6)

Answer 2

I found your notation a bit confusing, but I'll stick with it. First, note that (sqrt)3/2 = 1/2 of (sqrt)6; multiply by 4 under the radical and 1/2 outside of it to see this, making no net change. Now we have 1/2 (squrt)6 + 5 (sqrt)6, or 5.5(sqrt)6.