Algebra (urgent!)
posted by Shealyn .
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
Respond to this Question
Similar Questions

Math
Just need some help... Directions: Multiply or raise to the power as indicated... Then simplify the result. Assume all variables represent positive numbers. 1. 5(square root of 6) times twothirds(square root of 15)= 3 onethird (square … 
algebra
Multiply and simplify (9square root 6  4 square root 10) (square root 6  7 square root 10) I have been stumped and working on all day. Any suggestions? 
Algebra
I am supposed to "write each expression with a rational denominator" 1/thesqrootof 3. I follow the book's explanation, until it suggests dividing the sq. root of 3 by the square root of 3 times the square root of three. I do not understand … 
Algebra
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 … 
Math
Could someone please help me with this math problem? 
Algebra
Rationalize each expression by building perfect nth root factors for each denominator. Assume all variables represent positive quantities. I don’t understand how to compute these. Also I don’t have the square root sign so I typed … 
College Algebra
I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth root … 
College Algebra help please
I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth root … 
College Algebra
I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth root … 
Math simplifying mixed radicals
Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are supposed …