SOLUTION: I need assistance in figuring out the following: {{{8sqrt(2)(sqrt(8)-3sqrt(2)+7sqrt(32))}}} I have an algebra test tomorrow and nearly no one in my class really understands

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: I need assistance in figuring out the following: {{{8sqrt(2)(sqrt(8)-3sqrt(2)+7sqrt(32))}}} I have an algebra test tomorrow and nearly no one in my class really understands      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 176969: I need assistance in figuring out the following:
8sqrt%282%29%28sqrt%288%29-3sqrt%282%29%2B7sqrt%2832%29%29

I have an algebra test tomorrow and nearly no one in my class really understands the math material we are being tested on, so this would be extremely helpful and I would be veryyyyyyyy grateful for any help!
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(48564) About Me  (Show Source):
You can put this solution on YOUR website!
8sqrt(2)(sqrt(8)-3sqrt(2)+7sqrt(32)
-----------
Rule: sqrt(AB) = sqrt(A)*sqrt(B)
----------------
= 8 sqrt(16) - 3sqrt(2) + 7sqrt(16)*sqrt(2)
= 8*4 - 3sqrt(2) + 7*4*sqrt(2)
= 32 - 3sqrt(2) + 28sqrt(2)
= 32 + 25sqrt(2)
---------------------
Cheers,
Stan H.

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate:
%288sqrt%282%29%29%28sqrt%288%29-3sqrt%282%29%2B7sqrt%2832%29%29
Ok, the key thing here is to get all of the radicands (the numbers inside of the square root symbols) to = 2, if possible. Well, since you know that 8 and 32 are multiples of 2 this is possible. So here we go, step-by-step!
%288sqrt%282%29%29%28sqrt%284%2A2%29-3sqrt%282%29%2B7sqrt%2816%2A2%29%29
Now, sqrt%284%29+=+2 so you can move that outside of the radical but leave the 2 inside. And, sqrt%2816%29+=+4 so you can move that outside of the radical leaving the 2 inside:
%288sqrt%282%29%29%282sqrt%282%29-3sqrt%282%29%2B7%2A4sqrt%282%29%29 Multiply the 7*4 = 28
%288sqrt%282%29%29%282sqrt%282%29-3sqrt%282%29%2B28sqrt%282%29%29 In the second set of parentheses, collect all of the sqrt%282%29's together.
%288sqrt%282%29%29%2827sqrt%282%29%29 Finally, perform the indicated multiplication, do the numbers first (8*27 = 216) then the radicals (sqrt%282%29%2Asqrt%282%29+=+2 to get:
highlight%28216%2A2+=+432%29