# Thread: trying to relearn some concepts..

1. ## trying to relearn some concepts..

Been trying to refresh myself on my math stuffs and realized I forgot how to work with radicals. A good overview of how to work with radicals would be quite nice. Right now I'm working with dividing radicals and radicals in fractions. Any help would be greatly appreciated, as I'd really like to save myself a lot of time by simply refreshing myself on all of this. Thanks!

2. Hello,

Well, here are some properties :

$\displaystyle \sqrt{ab}=\sqrt{a} \times \sqrt{b}$

$\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

$\displaystyle \sqrt{a^2 b}=|a| \sqrt{b}$

You can retrieve all of these with the properties of the powers :

$\displaystyle \sqrt{a}=a^{\frac12}$

3. $\displaystyle \sqrt{a}=a^{\frac{1}{2}}$

Then just treat it the same as all of your exponential rules.
They work the same
Same with any other root, i.e. cubed root = $\displaystyle a^{\frac{1}{3}}$

4. ah okay, what about something like: 18 / sqrt(18) ?

5. $\displaystyle \frac{18}{18^{\frac{1}{2}}}$ Then with exponents you subtract the bottom exponent from the top so 1-1/2.
so the simplified would be $\displaystyle 18^{\frac{1}{2}} or \sqrt{18}$

6. And note that 18=2*3²

So $\displaystyle \sqrt{18}=\sqrt{3^2*2}=3 \sqrt{2}$