# Thread: Stuck on a square root problem

1. ## Stuck on a square root problem

Hi! I am stuck on my homework. I came across a problem I didn't know how to do and there isn't a single example like it in my book or notes. The problem is-

Find where the square root of x-3 over -2x-8 is real

Ashley

2. Originally Posted by aperkin2
Hi! I am stuck on my homework. I came across a problem I didn't know how to do and there isn't a single example like it in my book or notes. The problem is-

Find where the square root of x-3 over -2x-8 is real

Ashley
Hi

$\sqrt{\frac{x-3}{-2x-8}}$ is real when $\frac{x-3}{-2x-8} \geq 0$ which means

( $x-3 \geq 0$ and $-2x-8 > 0$) or ( $x-3 \leq 0$ and $-2x-8 < 0$)

3. Thank you so much for your help! That is starting to sound a little more familiar. Would the next step involve a number line or is there another step before that? Sorry, I'm just very lost here. Thanks for your help!

4. You just need to find :
- the set of x where $x-3 \geq 0$ and $-2x-8 > 0$
- the set of x where $x-3 \leq 0$ and $-2x-8 < 0$

And take the union of both sets. This is the answer you are asked

5. Oh I see! Thank you so much! I never would have figured that out on my own