Simplify $\displaystyle \sqrt{15+8i}$.

I got $\displaystyle 4+i$ or $\displaystyle -4 - i$, but only one of these solutions is correct.

Obviously $\displaystyle \sqrt{15+8i}>0$, but with my answers, wouldn't the pesky $\displaystyle i$ term disable you from checking whether the expression is greater or less than 0? After all, $\displaystyle i$ is not on the number line... I dunno, it just feels risky dealing with that $\displaystyle i$ term.

thanks