Need help with this Algebra problem...

[cherryblossom]

My dd and I have worked and reworked this problem and can't seem to get the answer in the solutions manual. Can someone PLEASE help? It deals with simplifying radicals and I will use these symbols ^/ to mean square root.

 

Ok, here is the problem:

 

3^/2(2^/2 - ^/6) . 4^/3 + 2

 

To interpret just in case the symbols are confusing:

 

3 square roots of 2 (2 square roots of 2 - square root of 6) times 4 square roots of 3 + 2

 

:confused:

[hoosiermom]

I'm assuming the last quantity is (4 square root 3) + 2 and not 4 square root (3 + 2).

 

If my assumption is correct, I get 36 square root 3 - 48 for the answer.

 

I first distributed 3 square root 2 thru first quantity and got 12 - 6 square root 3.

 

Then (12 - 6 square root 3) times (4 square root 3 + 2) gives me

 

(48 square root 3) + (24) - (24 x 3) - (12 square root 3) =

 

(48 square root 3) - (12 square root 3) + (24) - (72) =

 

36 square root 3 - 48

[Mama Geek]

I am using excel terminology because my brain will think that way, so your problem is written like this:

3*sqrt(2)*(2*sqrt(2)-sqrt(6))*4*sqrt(3)+2

 

The sqrt(6) = sqrt(3)*sqrt(2) so substitute that in

 

3*sqrt(2)*(2*sqrt(2)-sqrt(3)*sqrt(2))*4*sqrt(3)+2

 

(3*2*sqrt(2)^2-3*sqrt(2)^2*sqrt(3))*4*sqrt(3)+2

 

(3*2*2-3*2*sqrt(3))*4*sqrt(3)+2

 

(12-6*sqrt(3))*4*sqrt(3)+2

 

(12*4*sqrt(3)-6*4*sqrt(3)^2)+2

 

(48*sqrt(3)-6*4*3)+2

 

(48*sqrt(3)-72)+2

 

48*sqrt(3)-70

 

I double checked it on a spreadsheet, so this should be what you are looking for.

 

ETA the difference between my solution and hoosiermoms is the interpretation of where the +2 fits into the equation. Hope one of these two solutions help.

Edited January 19, 2011 by Mama Geek

[Belacqua]

Cherryblossom, are you familiar with Wolfram Alpha? It has come to my rescue countless times. It's also just fun to play with. :001_smile: