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Multiply. Write your answer in simplest form. $\newline$ $-\sqrt{2}(6 - \sqrt{5})$

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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}(6 - \sqrt{5})

Distribute $-\sqrt{2}$ : Distribute $-\sqrt{2}$ to both terms inside the parentheses.-\sqrt{\(2\)}(\(6 - \sqrt{ $5$ }) = -\sqrt{ $2$ }\cdot $6$ - \sqrt{ $2$ }\cdot(-\sqrt{ $5$ })
Multiply $-\sqrt{2}$ by $6$ : Multiply $-\sqrt{2}$ by $6$ . $\newline$ $-\sqrt{2} \times 6$ $\newline$ $= -6\sqrt{2}$
Multiply $-\sqrt{2}$ by $-\sqrt{5}$ : Multiply $-\sqrt{2}$ by $-\sqrt{5}$ .
$-\sqrt{2} \times (-\sqrt{5})$
= \sqrt{ $2$ } \times \sqrt{ $5$ } (since the product of two negatives is positive)
= \sqrt{ $2$ \times $5$ } (applying the product rule for radicals)
= \sqrt{ $10$ }
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $-6\sqrt{2} + \sqrt{10}$

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