Simplify the expression completely. $\newline$ $-3 \sqrt{64}-\sqrt{-9}+2 \sqrt{16}$ $\newline$ Answer:

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Q. Simplify the expression completely.

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-3 \sqrt{64}-\sqrt{-9}+2 \sqrt{16}

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Answer:

Question Prompt: Question prompt: Simplify the expression completely. $\newline$ $-3\sqrt{64} - \sqrt{-9} + 2\sqrt{16}$
Simplify Square Root of $64$ : Simplify the square root of $64$ . The square root of $64$ is $8$ because $8^2 = 64$ . $-3\sqrt{64}$ becomes $-3 \times 8$ .
Calculate Product of $-3$ and $8$ : Calculate the product of $-3$ and $8$ . $\newline$ Multiplying $-3$ by $8$ gives $-24$ . $\newline$ $-3 \times 8 = -24$ .
Simplify Square Root of $-9$ : Simplify the square root of $-9$ . The square root of $-9$ is not a real number; it is an imaginary number. The square root of $9$ is $3$ , and since we are taking the square root of a negative number, we use the imaginary unit $i$ . $\sqrt{-9}$ becomes $3i$ .
Simplify Square Root of $16$ : Simplify the square root of $16$ . $\newline$ The square root of $16$ is $4$ because $4^2 = 16$ . $\newline$ $2\sqrt{16}$ becomes $2 \times 4$ .
Calculate Product of $2$ and $4$ : Calculate the product of $2$ and $4$ . $\newline$ Multiplying $2$ by $4$ gives $8$ . $\newline$ $2 \times 4 = 8$ .
Combine Simplified Terms: Combine all the simplified terms. $\newline$ Combine $-24$ (from Step $2$ ), $3i$ (from Step $3$ ), and $8$ (from Step $5$ ). $\newline$ The expression becomes $-24 - 3i + 8$ .
Add $-24$ and $8$ : Add $-24$ and $8$ . $\newline$ Adding $-24$ and $8$ gives $-16$ . $\newline$ $-24 + 8 = -16$ .
Write Final Expression: Write the final simplified expression. $\newline$ The final expression is $-16 - 3i$ .