Answer
The value of the operation for the expression $2\sqrt{-49}+3\sqrt{-64}$ in the standard form is $38i$.
Work Step by Step
Consider the expression:
$2\sqrt{-49}+3\sqrt{-64}$
Rewrite the expression $2\sqrt{-49}+3\sqrt{-64}$ as $2\sqrt{49}\sqrt{-1}+3\sqrt{64}\sqrt{-1}$
As $i=\sqrt{-1}$
Therefore,
$\begin{align}
& 2\sqrt{49}\sqrt{-1}+3\sqrt{64}\sqrt{-1}=2\left( 7 \right)i+3\left( 8 \right)i \\
& =14i+24i
\end{align}$
Combine the real part and imaginary part separately and either add or subtract as required.
$14i+24i=38i$
So,
$2\sqrt{-49}+3\sqrt{-64}=38i$
Hence, the value of the operation for the expression $2\sqrt{-49}+3\sqrt{-64}$ in the standard form is $38i$.
