really hard fraction question HELP

**andyboy179** · December 18th 2009, 06:57 AM

$\frac{8}{2 - \sqrt{2}}$

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?

**dedust** · December 18th 2009, 07:04 AM

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

**andyboy179** · December 18th 2009, 07:05 AM

just did it but i can't work out how to write it so it comes up how i want it

**andyboy179** · December 18th 2009, 07:16 AM

is what i put for the answer right? 16+

, as the numerator and 6 as the denominator?

**dedust** · December 18th 2009, 07:28 AM

Originally Posted by andyboy179

is what i put for the answer right? 16+

, as the numerator and 6 as the denominator?

the denominator is $2^2 - (\sqrt{2})^2 = . . .$

**andyboy179** · December 18th 2009, 07:29 AM

Originally Posted by dedust

the denominator is $2^2 - (\sqrt{2})^2 = . . .$

how? could you please explain it?

**dedust** · December 18th 2009, 07:40 AM

Originally Posted by andyboy179

how? could you please explain it?

$\frac{8}{2 - \sqrt{2}} \times \frac{2 + \sqrt{2}}{2 + \sqrt{2}} = \frac{8(2 + \sqrt{2})}{(2 - \sqrt{2})(2 + \sqrt{2})}$
$= \frac{(16 + 8\sqrt{2})}{(2^2 + 2\sqrt{2} - 2\sqrt{2} + \sqrt{2}^2)} = \frac{(16 + 8\sqrt{2})}{(4-2)} = \frac{(16 + 8\sqrt{2})}{2} = 8 + 4\sqrt{2}$

**andyboy179** · December 18th 2009, 07:53 AM

i get told to do this at school for the denominator,

$really hard fraction question HELP-222221.jpg$

**dedust** · December 18th 2009, 07:59 AM

Originally Posted by andyboy179

i get told to do this at school for the denominator,

$Click image for larger version. Name: 222221.jpg Views: 56 Size: 25.0 KB ID: 14513$

the last entry in the 2nd column should be $-2$ , because
$(-\sqrt{2}) \times (+\sqrt{2}) = -{2}$

**andyboy179** · December 18th 2009, 08:02 AM

thankyou so much

Thread: really hard fraction question HELP

LinkBack

Thread Tools

Display

really hard fraction question HELP

Similar Math Help Forum Discussions

hard fraction!

hard fraction

hard fraction

Hard fraction question (Homework)

fraction hard!

Search Tags