Inequality with square root on both sides I have equation like this:
$$\sqrt{\vphantom{|}\ 3x^2-7x-20}<\sqrt{\vphantom{|}\ 8x+22}$$
I'm unsure how to solve it. I'm guessing I have to square both sides, but I don't know what happens with the inequality sign.
I guess there are four cases, depending on the sign of each side of the equation $(++,\ +-,\ -+,\ --)$.
And then I have to check if the solution fits the case, ie if both sides are of apropriate sign for the resulting interval.
But all this seems like a lot of work. There is an easier way, right?
How is it usually done?

"There is an easier way, right?"
Nope.
First things first: in order for these square root signs to even make sense, what's underneath them has to be positive. So, first order of business: work out for which values of $x$ both $3x^2-7x-20$ and $8x+22$ are positive.
Now, if $a$ and $b$ are positive numbers, then $\sqrt a < \sqrt b$ if and only if $a < b$. So once you've determined for which value of $x$ the inequality makes sense, you can just let $x$ be any such value, and just remove the square root signs. You'll end up with
$$3x^2-7x-20<8x+22$$
Now work out, out of the set of values of $x$ you found in the first part of the problem, which ones verify that inequality.
