Multiplying and Dividing radical expressions

Hey I'm on the last stretch of my math course and I have 19 more assignments ( sounds like a lot but I've already done almost 60 myself) and so far I'm not getting a very......decent grade. so please help me! I need this class to graduate!

1. √10 x √8
a √18
b 4√5
c √80
d none of the above

2. √5(8 + 3√6)
a 5√8 + 3√30
b 5√10
c 130
d none of the above

3. (4-√3)(12+5√3)
a 33
b 33- 32√3
c 63 + 8√3
d 33 + 8√3

4. (5+√3)(5-√3
a 22
b 28
c 22 - 10√3
d 25 - 12√3

5. Identify the conjugate 4 + √7
a √7 - 4
b 7 + √4
c 4 + √7
d 4 - √7

6 rationalize the denominator of √18/√3
a 6
b 2√3/3
c 3√3/2
d 2/√6

7 rationalize the denominator of 5/√3
a 5√3/3
b 5/3
c √3/3
d 5

8 rationalize the denominator of 4/5+√2
a 20 - √2/23
b 20 - 4√2/27
c 20-4√2/23
d 5 - 4√2/27

9 Create your own binomial expression with a radical in the second term. Identify its conjugate and explain, in complete sentences, why it is the conjugate. Multiply your original binomial expression and its conjugate. What happened to the radicals and why?

1.
√10 * √8
= √(10 * 8)
= √80
= √(16 * 5)
= √16√5
= (b) 4√5


2.
√5(8 + 3√6)
= 8√5 + 3√6√5
= 8√5 + 3(√6√5)
= 8√5 + 3√(6*5)
= (a) 8√5 + 3√30


3.
(4 - √3)(12 + 5√3)
= 4(12 + 5√3) - √3(12 + 5√3)
= 48 + 20√3 - 12√3 - 5√3√3
= 48 + 20√3 - 12√3 - 5(√3√3)
= 48 + 20√3 - 12√3 - 5(3)
= 48 + 20√3 - 12√3 - 15
= (d) 33 + 8√3


4.
(5+√3)(5-√3)
= 5(5-√3) + √3(5-√3)
= 25 - 5√3 + 5√3 - √3√3
= 25 - 5√3 + 5√3 - 3
= (a) 22


5.
conjugate of (a + b) = (a - b):
(d) 4 - √7


6.
rationalize the denominator of √18/√3:
√18 / √3
= (√18√3) / (√3√3)
= (√18√3) / 3
= √(18*3) / 3
= √54 / 3
= √(9*6) / 3
= (√9√6) / 3
= (3√6) / 3
= √6 [did you make a typo and forget the √ sign in option (a)?]