really hard fraction question HELP

• Dec 18th 2009, 07:57 AM
andyboy179
really hard fraction question HELP
$\frac{8}{2 - \sqrt{2}}$

is this right, $\frac{8}{2 - \sqrt{2}} X \frac{2 + \sqrt{2}}{2 + \sqrt{2}}$ = 16+ $8\sqrt{2}$, as the numerator and 6 as the dinominator?
• Dec 18th 2009, 08:04 AM
dedust
Quote:

Originally Posted by andyboy179
$\frac{8}{2 - \sqrt{2}}$

is this right, $\frac{8}{2 - \sqrt{2}} \times \frac{2 + \sqrt{2}}{2 + \sqrt{2}}$ = $\frac{16}+ 3\sqrt{2}}$

$= \frac {16 + 8\sqrt{2}}{2^2 - (\sqrt{2})^2} = . . .$

multiply it term by term and then simplify
• Dec 18th 2009, 08:05 AM
andyboy179
just did it but i can't work out how to write it so it comes up how i want it
• Dec 18th 2009, 08:16 AM
andyboy179
is what i put for the answer right? 16+http://www.mathhelpforum.com/math-he...e10ec23f-1.gif, as the numerator and 6 as the denominator?
• Dec 18th 2009, 08:28 AM
dedust
Quote:

Originally Posted by andyboy179
is what i put for the answer right? 16+http://www.mathhelpforum.com/math-he...e10ec23f-1.gif, as the numerator and 6 as the denominator?

the denominator is $2^2 - (\sqrt{2})^2 = . . .$
• Dec 18th 2009, 08:29 AM
andyboy179
Quote:

Originally Posted by dedust
the denominator is $2^2 - (\sqrt{2})^2 = . . .$

how? could you please explain it?
• Dec 18th 2009, 08:40 AM
dedust
Quote:

Originally Posted by andyboy179
how? could you please explain it?

$\frac{8}{2 - \sqrt{2}} \times \frac{2 + \sqrt{2}}{2 + \sqrt{2}} = \frac{8(2 + \sqrt{2})}{(2 - \sqrt{2})(2 + \sqrt{2})}$
$= \frac{(16 + 8\sqrt{2})}{(2^2 + 2\sqrt{2} - 2\sqrt{2} + \sqrt{2}^2)} = \frac{(16 + 8\sqrt{2})}{(4-2)} = \frac{(16 + 8\sqrt{2})}{2} = 8 + 4\sqrt{2}$
• Dec 18th 2009, 08:53 AM
andyboy179
i get told to do this at school for the denominator,

Attachment 14513
• Dec 18th 2009, 08:59 AM
dedust
Quote:

Originally Posted by andyboy179
i get told to do this at school for the denominator,

Attachment 14513

the last entry in the 2nd column should be $-2$, because
$(-\sqrt{2}) \times (+\sqrt{2}) = -{2}$
• Dec 18th 2009, 09:02 AM
andyboy179
thankyou so much