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

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Simplify radical expressions using the distributive property

Full solution

Q. Multiply. Write your answer in simplest form.

\newline

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

Distribute $\sqrt{2}$ : Distribute $\sqrt{2}$ across the terms inside the parentheses. $\sqrt{2}(5 - \sqrt{5}) = \sqrt{2} \times 5 + \sqrt{2} \times (-\sqrt{5})$
Multiply by $5$ : Multiply $\sqrt{2}$ by $5$ . $\sqrt{2} \times 5 = 5\sqrt{2}$
Multiply by $-\sqrt{5}$ : Multiply $\sqrt{2}$ by $-\sqrt{5}$ . $\sqrt{2} \times (-\sqrt{5}) = -\sqrt{2 \times 5} = -\sqrt{10}$
Combine to get final answer: Combine the two results to get the final answer. $5\sqrt{2} - \sqrt{10}$

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