SOLUTION: Could someone help with this radical? I am having troubles understanding how to do this? (√{6}+2√{2})(4√{6}-3√{2}) Could you help me step by step on th

Algebra ->  Radicals -> SOLUTION: Could someone help with this radical? I am having troubles understanding how to do this? (√{6}+2√{2})(4√{6}-3√{2}) Could you help me step by step on th      Log On


   

Question 136727: Could someone help with this radical? I am having troubles understanding how to do this?
(√{6}+2√{2})(4√{6}-3√{2})
Could you help me step by step on this?
The other one that seems a little easier that I can not figure is
√{81}x12y8z10}
I know that the √ of 81 is 9 but how do I figure out the exponents?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(√{6}+2√{2})(4√{6}-3√{2})
Use FOIL:
F: =4*6 = 24
O: =-3sqrt12 = -6sqrt(3)
I: = 4sqrt(12) = 8sqrt(3)
L: = -6*2 = -12
---------------
Combine to get: 12 + 2sqrt(3)
=========================================
The other one that seems a little easier that I can not figure is
√{81}{x12y8z10}
= 9x^12y^8z^10
=========================================
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%286%29%2B2sqrt%282%29%29%284sqrt%286%29-3sqrt%282%29%29

Use FOIL just like you would on something like %28x-2%29%28x%2B4%29

First: sqrt%286%29%2A4sqrt%286%29=4%2A6=24

Outside: sqrt%286%29%2A-3sqrt%282%29=-3sqrt%2812%29=-3%2A2sqrt%283%29=-6sqrt%283%29

Inside: 2sqrt%282%29%2A4sqrt%286%29=8sqrt%2812%29=8%2A2sqrt%283%29=16sqrt%283%29

Last: 2sqrt%282%29%2A-3sqrt%282%29=-6%2A2=-12

Add 'em up:
24-6sqrt%283%29%2B16sqrt%283%29-12
12%2B10sqrt%283%29

sqrt%2881x%5E12y%5E8z%5E10%29

Remember that sqrt%28x%29=x%5E%281%2F2%29, and x%5E%28m%2Fn%29=root%28n%2Cx%5Em%29

so

sqrt%2881x%5E12y%5E8z%5E10%29=9x%5E6y%5E4z%5E5