Radical trouble?

[Smokinoakum]

Hi everyone...I have a problem that I have for my online class that I thought I knew, but the software is saying I'm wrong. Could someone please straighten me out please!

The problem states this...

Rationalize the denominator.

?35-5 / ?35 = this is the answer I came out with 6?35 / 7 and the software says the answer is 7-?35 / 7

Could someone please help me understand. I punched in the original equation and got the decimal point number= 5.070925528 for both my answer, and the original question, so that makes things really confusing.

Neil

 

[galactus]

$\displaystyle \frac{(\sqrt{35}-5)}{\sqrt{35}}\cdot \frac{\sqrt{35}}{\sqrt{35}}$

$\displaystyle \frac{35-5\sqrt{35}}{35}$

$\displaystyle 1-\frac{\sqrt{35}}{7}=\frac{7-\sqrt{35}}{7}$

 

[Smokinoakum]

$\displaystyle \frac{(\sqrt{35}-5)}{\sqrt{35}}\cdot \frac{\sqrt{35}}{\sqrt{35}}$

$\displaystyle \frac{35-5\sqrt{35}}{35}$

$\displaystyle 1-\frac{\sqrt{35}}{7}=\frac{7-\sqrt{35}}{7}$

I understood everything except the last line...How do you get the $\displaystyle 1-\frac{\sqrt{35}}{7}=\frac{7-\sqrt{35}}{7}$ and what happened to the -5

 

[lookagain]

Smokinoakum, try this:

$\displaystyle \frac{(\sqrt{35}-5)}{\sqrt{35}}\cdot \frac{\sqrt{35}}{\sqrt{35}} =$

$\displaystyle \frac{35-5\sqrt{35}}{35} =$

$\displaystyle \frac{5(7 - \sqrt{35})}{5(7)} =$

$\displaystyle \frac{7-\sqrt{35}}{7}$