Let's simplify the given expression step by step:
[tex]\[ 5 \sqrt{49} - \sqrt{-36} \][/tex]
First, we'll simplify each part separately.
1. Simplify [tex]\( 5 \sqrt{49} \)[/tex]:
[tex]\[
\sqrt{49} = 7
\][/tex]
Hence,
[tex]\[
5 \sqrt{49} = 5 \times 7 = 35
\][/tex]
2. Simplify [tex]\(\sqrt{-36}\)[/tex]:
The square root of a negative number involves an imaginary unit [tex]\(i\)[/tex] where [tex]\(i = \sqrt{-1}\)[/tex].
[tex]\[
\sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i
\][/tex]
Now, we combine these simplified parts back into the original expression:
[tex]\[ 5 \sqrt{49} - \sqrt{-36} = 35 - 6i \][/tex]
So, the simplified expression as a complex number is:
[tex]\[ 35 - 6i \][/tex]
Therefore, the correct answer is:
[tex]\[ 35 - 6i \][/tex]
