Hey!
First we'll find the region for [tex] \sqrt{x} [/tex].
[tex] \sqrt{x} [/tex] is real for [tex]x \geq 0[/tex].
So, the real region for [tex] \sqrt{x} [/tex] is [tex]x \geq 0[/tex]
Now, we'll simplify the [tex] \sqrt{x} \ \textgreater \ 6[/tex] by first squaring both sides.
Old Equation :
[tex] \sqrt{x} \ \textgreater \ 6[/tex]
New Equation {Added Square Both Sides} :
[tex]( \sqrt{x} )^{2} \ \textgreater \ 6^{2} [/tex]
Solution {New Equation Solved} :
x > 36
So, this means that the solution to [tex] \sqrt{x} \ \textgreater \ 6[/tex] is x > 36.
Hope this helps!
- Lindsey Frazier ♥