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

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Simplify radical expressions using the distributive property

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Q. Multiply. Write your answer in simplest form.

\newline

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

Distribute $-\sqrt{2}$ : Distribute $-\sqrt{2}$ to both terms inside the parentheses. $\newline$ -\sqrt{2}(-5 + \sqrt{2})\(\newline= -\sqrt{2} \times (-5) + -\sqrt{2} \times \sqrt{2}\)
Multiply $-\sqrt{2}$ by $-5$ : Multiply $-\sqrt{2}$ by $-5$ . $\newline$ $-\sqrt{2} \times (-5) = 5\sqrt{2}$
Multiply $-\sqrt{2}$ by $\sqrt{2}$ : Multiply $-\sqrt{2}$ by $\sqrt{2}$ . $\newline$ $-\sqrt{2} \times \sqrt{2} = -2$ $\newline$ This is because the square root of a number times itself equals the number.
Combine the results: Combine the results from Step $2$ and Step $3$ . $5\sqrt{2} - 2$ This is the simplest form of the expression.

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