#### Answer

$10-4i$

#### Work Step by Step

Since $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b},$ the given expression, $
(4+\sqrt{-9})+(6-\sqrt{-49})
,$ is equivalent to
\begin{align*}
&
(4+\sqrt{-1}\cdot\sqrt{9})+(6-\sqrt{-1}\cdot\sqrt{49})
\\&=
(4+\sqrt{-1}\cdot3)+(6-\sqrt{-1}\cdot7)
\\&=
(4+3\sqrt{-1})+(6-7\sqrt{-1})
.\end{align*}
Since $i=\sqrt{-1},$ the expression above is equivalent to
\begin{align*}
(4+3i)+(6-7i)
.\end{align*}
Removing the grouping symbols, the expression above is equivalent to
\begin{align*}
4+3i+6-7i
.\end{align*}
Combining the real parts and the imaginary parts, the expression above is equivalent to
\begin{align*}
&
(4+6)+(3i-7i)
\\&=
10+(-4i)
\\&=
10-4i
.\end{align*}
Hence, the simplified form of the given expression is $
10-4i
$.