Algebra (urgent!)
posted by Shealyn on .
I am a bit confused about conjugates in algebra. I am supposed to multiply 8/(the square root of two + 4) by the square root of 2 4. My math book then goes on to simplify this to (8 times the square root of two minus 32) divided by (24 times the square root of two plus 4 times the square root of 2 minus 16). I do not see how the bottom part came to be. Could someone offer an explanation, please?

8/(sqrt2 + 4)
multiply top and bottom by (sqrt 2 4) to get rid of the sqrt on the bottom because remember:
(ab)(a+b) = a^2  b^2
thereby squaring any square roots that might have been in b
8/(sqrt 2 + 4) * (sqrt 24)/(sqrt 24)
= 8 (sqrt 2  4) / [ (sqrt 2)^2  16 ]
= (8 sqrt 2  32) / [216]
= (8 sqrt 2  32) / 14
= (16  4 sqrt 2 / 7 
By the way your math book did the
(ab)(a+b) by FOIL
a^2 + ab ab  b^2 which is a^2b^2
but I know and you should know that
(ab)(a+b) = a^2  b^2
without going through the FOIL 
Squareroot of A* square root of AB ^2