Multiply. Write your answer in simplest form. sqrt 2(-9 + sqrt 3) ______

Distribute sqrt(2): Distribute sqrt(2) to both terms inside the parentheses. sqrt(2)(-9 + sqrt(3)) = sqrt(2)*(-9) + sqrt(2)*(sqrt(3))Multiply -9: Multiply sqrt(2) by -9. sqrt(2) * (-9) = -9 * sqrt(2)Multiply sqrt(3): Multiply sqrt(2) by sqrt(3). sqrt(2) * sqrt(3) Apply the product rule of radicals. = sqrt(2 * 3) = sqrt(6)Combine the results: Combine the results from Step 2 and Step 3. -9 * sqrt(2) + sqrt(6) This is the simplest form of the expression.

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{2}(-9 + \sqrt{3})$

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Algebra 2

Simplify radical expressions using the distributive property

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{2}(-9 + \sqrt{3})

Distribute $\sqrt{2}$ : Distribute $\sqrt{2}$ to both terms inside the parentheses. $\sqrt{2}(-9 + \sqrt{3})$ = $\sqrt{2}$ $-9$ + $\sqrt{2}$ $\sqrt{3}$
Multiply $-9$ : Multiply $\sqrt{2}$ by $-9$ . $\newline$ $\sqrt{2} \times (-9)$ $\newline$ $= -9 \times \sqrt{2}$
Multiply $\sqrt{3}$ : Multiply $\sqrt{2}$ by $\sqrt{3}$ . $\sqrt{2} \times \sqrt{3}$ Apply the product rule of radicals. $= \sqrt{2 \times 3}$ $= \sqrt{6}$
Combine the results: Combine the results from Step $2$ and Step $3$ . $\newline$ $-9 \times \sqrt{2} + \sqrt{6}$ $\newline$ This is the simplest form of the expression.