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Multiply. Write your answer in simplest form. $\newline$ $-\sqrt{3}(3 - \sqrt{5})$

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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}(3 - \sqrt{5})

Distribute $-\sqrt{3}$ : Distribute $-\sqrt{3}$ to both terms inside the parentheses.-\sqrt{\(3\)}(\(3 - \sqrt{ $5$ }) = -\sqrt{ $3$ }\cdot $3$ - \sqrt{ $3$ }\cdot(-\sqrt{ $5$ })
Multiply $-\sqrt{3}$ by $3$ : Multiply $-\sqrt{3}$ by $3$ . $\newline$ $-\sqrt{3} \times 3$ $\newline$ $= -3\sqrt{3}$
Multiply $-\sqrt{3}$ by $-\sqrt{5}$ : Multiply $-\sqrt{3}$ by $-\sqrt{5}$ . $\newline$ $-\sqrt{3} \times (-\sqrt{5})$ $\newline$ = $\sqrt{3} \times \sqrt{5}$ $\newline$ = $\sqrt{3 \times 5}$ $\newline$ = $\sqrt{15}$
Combine the results: Combine the results from the previous steps. $\newline$ $-3\sqrt{3} + \sqrt{15}$ $\newline$ This is the simplest form, as there are no like terms to combine and the square roots cannot be simplified further.

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