9th grade Algebra. I just don't get adding and multiplying square roots? 10 points!

First, explain to me this:
3√6+√24

How would you even begin to work that out?
My Algebra teacher can't teach worth a crap and I'm so confused!
And something like:
√3(5√3-2√6)

None of this makes sense to me :(

3√6 + √24
= 3√6 + √4√6
= 3√6 + 2√6
= 5√6

√3(5√3-2√6)
= 5√3√3 - 2√6√3
= 5(3) - 2√(3*2)√3
= 15 - 2√3√2√3
= 15 - 2(3)√2
= 15 - 6√2

3√6 + v24

3√6 + (√6*√4)

3√6 + 2√6

answer = 5√6

√3(5√3-2√6)

when you times a rt by the same rt you get what's inside

√3 * 5 √3 = 3 * 5 = 15
-
√3 * -2√6
= - 2 √18
=-2√9√2
= 6√2


15 - 6√2