Multiply. Write your answer in simplest form. sqrt 2(-5 + sqrt 5) ______

Distribute sqrt(2): Distribute sqrt(2) to both terms inside the parentheses. sqrt(2)(-5 + sqrt(5)) = sqrt(2)*(-5) + sqrt(2)*(sqrt(5))Simple Multiplication: We have: sqrt(2) * (-5) This is a simple multiplication of a radical with a real number. sqrt(2) * (-5) = -5 * sqrt(2)Multiply Radicals: Now, we multiply the radicals: sqrt(2) * sqrt(5) Apply the product rule of radicals. sqrt(2) * sqrt(5) = sqrt(2 * 5) = sqrt(10)Combine Results: Combine the results from the previous steps to get the final answer. -5 * sqrt(2) + sqrt(10) This is the simplest form, as no further simplification is possible.

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{2}(-5 + \sqrt{5})$

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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}(-5 + \sqrt{5})

Distribute $\sqrt{2}$ : Distribute $\sqrt{2}$ to both terms inside the parentheses. $\newline$ $\sqrt{2}(-5 + \sqrt{5})$ $\newline$ = $\sqrt{2}\cdot(-5) + \sqrt{2}\cdot(\sqrt{5})$
Simple Multiplication: We have: $\newline$ $\sqrt{2} \times (-5)$ $\newline$ This is a simple multiplication of a radical with a real number. $\newline$ $\sqrt{2} \times (-5)$ $\newline$ = $-5 \times \sqrt{2}$
Multiply Radicals: Now, we multiply the radicals: $\newline$ $\sqrt{2} \times \sqrt{5}$ $\newline$ Apply the product rule of radicals. $\newline$ $\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} = \sqrt{10}$
Combine Results: Combine the results from the previous steps to get the final answer. $\newline$ $-5 \times \sqrt{2} + \sqrt{10}$ $\newline$ This is the simplest form, as no further simplification is possible.