#### Answer

$-|x|$

#### Work Step by Step

We know that $\sqrt x^{2}=|x|$, because $|x|^{2}=x\times x=x^{2}$.
Therefore, $-\sqrt x^{2}=-(|x|)=-|x|$.
We must include the absolute value sign to ensure that the square root is positive, since we know that the square root of a real number cannot be negative.