I've never had troubles in math before, but now we're doing exponents and radicals and I'm really stuck. Help?

Question

I'm a grade nine student in an advanced math program, working at (I think) a grade 10 academic level. We're doing radicals and exponents, and I understand the basics of both, I just have troubles with harder questions. For example:
SIMPLIFY
4*(square root of 2)*([square root of 2]+[square root of 18])
According to my teacher and the answers in the back of my math textbook the answer to this question is 32? Could anybody explain this and just give me any help you can on exponents and radicals in general? And PLEASE don't use really confusing words, or terms, or anything - I just started this unit and I'm really lost, fancy mathematical terminology really won't help.

Answer 1

4* sqrt(2)*(sqrt(2)+sqrt(18))
4*sqrt(2)* (sqrt(2) +3* sqrt(2))
substitute sqrt(2) with x.
4x*(x+3x)
4x*4x
16x*x
Substitute back.
16*sqrt(2)*sqrt(2)
16*2
32

There is my explanation.

Answer 2

Fear not! If your brain got you into advanced math you will get it soon enough. Just remember all your rules and with a little practice you will be able to use them in all sorts of new places in the future. Here is your problem

x = 4 √2 (√2 + √18)

First lets simplify the second radical, choosing to extract a perfect square (and being coincidentally left with a 2)!

√18 = √(9*2) = √9 √2 = 3 √2

Then distribute the √2 into the bracketed term

x = 4 (√2 √2 + 3 √2 √2)

Now we know that √2 √2 = 2 so

x = 4 (2 + 3 * 2)
x = 4 (8)
x = 32

Answer 3

ok - first i'd send you to somewhere like www.purplemath.com
if my kids are confused over the years its helped as it has clear explanations

first : sqrt2 * sqrt 2 = sqrt4 = 2
so generally sqrtA * sqrt A = A


4*(square root of 2)*([square root of 2]+[square root of 18])
4*(sqrt 2)*([sqrt of 2]+[sqrt of 9 * 2])
but sqrt of 9 = 3 and sqrt 2*[sqrt of 2] = 2

4*(sqrt 2)*([sqrt of 2]+ 3 * [sqrt of 2])
ok so now we distribute
ill do it in steps for you
4*(sqrt 2)*(sqrt of 2) = 4 * 2 = 8 as(sqrt 2)*([sqrt of 2) = 2

4*(sqrt 2)*3 * [sqrt of 2] = 12 * 2=24

8+24 = 32
hope that helps
practice some out by writing them and you'll get it!

Answer 4

4*(square root of 2)*([square root of 2]+[square root of 18])

expand it to get

1st part:
4sqrt(2){sqrt(2)} = 4(2) =8

second part:
4sqrt(2){sqrt(18)} = 4 sqrt(36) = 4(6) =24

24 +8 = 32

Answer 5

4*(square root of 2)*([square root of 2]+[square root of 18])
=4 sqrt(2) (sqrt(2)+3sqrt(2))
=4 sqrt(2) (4sqrt(2))
=4*4*2=32

Answer 6

4sqrt2[sqrt2+sqrt18]=4sqrt2[sqrt2+sqrt2sqrt9]
4*2+4*2*3=8+4*6=8+24=32