# Thread: I just don't understand radicals:

1. ## I just don't understand radicals:

How does
$\displaystyle -(\frac{\sqrt{3}}{6}) - (\frac{\sqrt{3}}{3}) = -(\frac{\sqrt{3}}{2})$

Here's my work:
$\displaystyle -(\frac{\sqrt{3}}{6}) - (\frac{\sqrt{3}}{3})$
$\displaystyle -(\frac{\sqrt{3}}{6}) - (\frac{2}{2}*\frac{\sqrt{3}}{3})$
$\displaystyle -(\frac{\sqrt{3}}{6}) - (2*\frac{\sqrt{3}}{6})$
$\displaystyle -(\frac{\sqrt{3}}{6})$

I get so confused when I have to manipulate radicals. Any ideas on what I can do to fix it?

2. The line before last ... check again!

3. $\displaystyle -(\frac{\sqrt{3}}{6}) - (2*\frac{\sqrt{3}}{6})$ BAD...

Actually, I think I mistyped it into the forum.  Even though I mistyped it, I think it is still the same. I'm not sure where I'm going wrong with it. Is there a 'radical tutorial' website that'll be helpful?[/edit]

$\displaystyle -(\frac{\sqrt{3}}{6}) - (\frac{2\sqrt{3}}{6})$
$\displaystyle -(\frac{\sqrt{3}}{6})$

I know the denominator should eventually be a 2, but I just do see that happening at any time of simplifying the solution.

4. Originally Posted by EMyk01
$\displaystyle -(\frac{\sqrt{3}}{6}) - (2*\frac{\sqrt{3}}{6})$ BAD...

Actually, I think I mistyped it into the forum.  Even though I mistyped it, I think it is still the same. I'm not sure where I'm going wrong with it. Is there a 'radical tutorial' website that'll be helpful?[/edit]

$\displaystyle -(\frac{\sqrt{3}}{6}) - (\frac{2\sqrt{3}}{6})$
$\displaystyle -(\frac{\sqrt{3}}{6})$

I know the denominator should eventually be a 2, but I just do see that happening at any time of simplifying the solution.
$\displaystyle -\left(\frac{\sqrt{3}}{6}\right)-2\left(\frac{\sqrt{3}}{6}\right)=(-1-2)\frac{\sqrt{3}}{6}=how\ many\ \frac{\sqrt{3}}{6}\ ?$

5. Originally Posted by Archie Meade
$\displaystyle -\left(\frac{\sqrt{3}}{6}\right)-2\left(\frac{\sqrt{3}}{6}\right)=(-1-2)\frac{\sqrt{3}}{6}=how\ many\ \frac{\sqrt{3}}{6}\ ?$

Okay, I think I understand. You were able to pull out the -1 and the -2 from the $\displaystyle \frac{\sqrt{3}}{6}$

In doing so, I have $\displaystyle -3*\frac{\sqrt{3}}{6}$

Then solving the rest of the problem, it should look like:

$\displaystyle \frac{-3}{1}(\frac{\sqrt{3}}{6})$

-3 and 6 cancel out and I get my final answer of:
$\displaystyle -\frac{\sqrt{3}}{2}$

Is that correct?

 I seem to have a hard time doing this latex coding stuff. Please excuse me while I try to fix it.
[edit again] Okay, hopefully that fixed it.

6. Originally Posted by EMyk01
Okay, I think I understand. You were able to pull out the -1 and the -2 from the $\displaystyle \frac{\sqrt{3}}{6}$

In doing so, I have $\displaystyle -3*\frac{\sqrt{3}}{6}$

Then solving the rest of the problem, it should look like:

$\displaystyle \frac{-3}{1}\left(\frac{\sqrt{3}}{6}\right)$

-3 and 6 cancel out and I get my final answer of:

$\displaystyle -\frac{\sqrt{3}}{6}$

Is that correct?
But you were wondering why the answer should be $\displaystyle -\frac{\sqrt{3}}{2}$

$\displaystyle -3\frac{\sqrt{3}}{6}=-\frac{3}{6}\sqrt{3}=?$

7. That was one of those mistakes that I fixed in the process. I said, "-3 and 6 cancel out" but in the math, I didn't cancel it out. So I now have the edited version, $\displaystyle -\frac{\sqrt{3}}{2}$ which is the end answer that I was looking for. I think I'm finished now...

8. Ah! sorry... yes, Latex takes getting used to at the beginning. Use "Preview" until you're ready to post.