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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{2}(-6 - \sqrt{3})$

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Simplify radical expressions using the distributive property

Full solution

Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{2}(-6 - \sqrt{3})

Distribute $\sqrt{2}$ : We need to distribute $\sqrt{2}$ across the terms inside the parentheses. $\sqrt{2}(-6 - \sqrt{3}) = \sqrt{2} \times -6 + \sqrt{2} \times -\sqrt{3}$
Multiply by $-6$ : Now we multiply $\sqrt{2}$ by $-6$ . $\sqrt{2} \times -6 = -6\sqrt{2}$
Multiply by $-\sqrt{3}$ : Next, we multiply $\sqrt{2}$ by $-\sqrt{3}$ . $\newline$ $\sqrt{2} \times -\sqrt{3} = -\sqrt{2 \times 3} = -\sqrt{6}$
Combine the products: Combine the two products to get the final answer. $\newline$ $-6\sqrt{2} - \sqrt{6}$

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