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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{2}(4 - \sqrt{5})$

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Simplify radical expressions using the distributive property

Full solution

Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{2}(4 - \sqrt{5})

Distribute $\sqrt{2}$ : Distribute $\sqrt{2}$ across the terms inside the parentheses. $\newline$ $\sqrt{2}(4 - \sqrt{5}) = \sqrt{2} \times 4 - \sqrt{2} \times \sqrt{5}$
Multiply by $4$ : Multiply $\sqrt{2}$ by $4$ . $\newline$ $\sqrt{2} \times 4 = 4\sqrt{2}$
Multiply by $\sqrt{5}$ : Multiply $\sqrt{2}$ by $\sqrt{5}$ . $\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} = \sqrt{10}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $4\sqrt{2} - \sqrt{10}$
Write final answer: Write the final answer in simplest form. $\newline$ The expression is already in simplest form, so the final answer is $4\sqrt{2} - \sqrt{10}$ .

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