We have \(x+x^2+\sqrt{x}=2457.\)

The best thing to do is to set boundary parenthesis.

Let's try an integer value of \(x\), denote 36, which is 6^2. Plugging it in, we get \(36+36^2+6=1338\), so we have to go a bit higher.

Tring 49 gives us: \(49+49^2+7=2457\)-Yes!

Thus, the answer is \(\boxed{49}.\)

In these type of problems...it's best to set boundaries to minimize the range of the values. You could try moving the \(x\)'s to the other side, but that could go ugly.