\sqrt((-6-5)^(2)+[-8-(-12)]^(2))

Answer 1

We need to simplify the expression inside the square root:

\begin{align*}
(-6-5)^2 + [-8-(-12)]^2 &= (-11)^2 + [-8+12]^2 \\
&= 121 + [4]^2 \\
&= 121 + 16 \\
&= 137
\end{align*}

So the simplified expression is $\sqrt{137}$.