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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{3}(-8 - \sqrt{3})$

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Simplify radical expressions using the distributive property

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{3}(-8 - \sqrt{3})

Distribute $\sqrt{3}$ : Distribute $\sqrt{3}$ to both terms inside the parentheses. $\sqrt{3}(-8 - \sqrt{3})$ = $\sqrt{3} \times (-8) - \sqrt{3} \times \sqrt{3}$
Multiply by $-8$ : Multiply the square root of $3$ by $-8$ . $\sqrt{3} \times (-8) = -8 \times \sqrt{3}$
Square root of $3$ : Multiply the square root of $3$ by itself. $\newline$ $\sqrt{3} \times \sqrt{3} = 3$ $\newline$ This is because the square root of a number multiplied by itself gives the original number.
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $-8 \times \sqrt{3} - 3$

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