Multiply. Write your answer in simplest form. sqrt 2(10 + sqrt 5) ______

Distribute sqrt(2): Distribute sqrt(2) to both terms inside the parentheses. sqrt(2)(10 + sqrt(5)) = sqrt(2)*10 + sqrt(2)*sqrt(5)Multiply by 10: Multiply sqrt(2) by 10. sqrt(2) * 10 = 10sqrt(2)Multiply by sqrt(5): Multiply sqrt(2) by sqrt(5). sqrt(2) * sqrt(5) Apply the product rule of radicals. = sqrt(2 * 5) = sqrt(10)Combine the results: Combine the results from Step 2 and Step 3. 10sqrt(2) + sqrt(10) This is the simplest form since there are no like terms to combine and the radicals cannot be simplified further.

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{2}(10 + \sqrt{5})$

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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}(10 + \sqrt{5})

Distribute $\sqrt{2}$ : Distribute $\sqrt{2}$ to both terms inside the parentheses. $\sqrt{2}(10 + \sqrt{5}) = \sqrt{2}\cdot 10 + \sqrt{2}\cdot \sqrt{5}$
Multiply by $10$ : Multiply $\sqrt{2}$ by $10$ . $\newline$ $\sqrt{2} \times 10$ $\newline$ = $10\sqrt{2}$
Multiply by $\sqrt{5}$ : Multiply $\sqrt{2}$ by $\sqrt{5}$ . $\sqrt{2} \times \sqrt{5}$ Apply the product rule of radicals. $= \sqrt{2 \times 5}$ $= \sqrt{10}$
Combine the results: Combine the results from Step $2$ and Step $3$ . $\newline$ $10\sqrt{2} + \sqrt{10}$ $\newline$ This is the simplest form since there are no like terms to combine and the radicals cannot be simplified further.