Help with multiplying radicals, cannot seem to understand it.

(√3+1)(5√3+1)
and
√5 ( 9√3 – 6√25)

Don't let the radical signs confuse you. The first problem is:
√3*5√3 + √3*1 + 1*5√3 + 1*1.

√3*5√3 = 5*3 = 15 (since √3*√3 = 3)
√3 + 5√3 = 6√3 (you have 1 + 5 √3's). If that confuses you, imagine the √3 was a variable, like x. You would have 6x.
The last term is obviously 1. So the answer would be 6√3 + 16.

The 2nd problem is similar. You can simplify 6√25 to 6*5 since √25 = 5. Rewrite it as:
√5 ( 9√3 – 30) and multiply it out:
9*√3*√5 - 30*√5
Note that √3*√5 = (3*5)^(1/2) = √15
This gives you: 9√15 - 30√5

1. Distribute:
(√3+1)(5√3+1) = √3(5√3+1) + 1(5√3+1) = 15+√3 + 5√3 + 1 = 16 + 6√3
(FOIL it, if you've learned it that way.)

2. Distribute:
√5 ( 9√3 – 6√25) = 9√3*√5 - 6√25*√5 = 9√15 - 30√5

5sqrt(3*3)+sqrt(3)*1+1*5sqrt(3)+1*1
5sqrt(9)+sqrt(3)+5sqrt(3)+1
5*3+sqrt(3)+5sqrt(3)+1
15+6sqrt(3)+1
16+6sqrt(3)

9sqrt(5*3)-6sqrt(5*25)
9sqrt(15)-6sqrt(125)
9sqrt(15)-6*5sqrt(5)
9sqrt(15)-30sqrt(5)