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

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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}(6 - \sqrt{2})

Distribute $\sqrt{2}$ : Distribute $\sqrt{2}$ across the terms inside the parentheses. $\sqrt{2}(6 - \sqrt{2}) = \sqrt{2} \times 6 - \sqrt{2} \times \sqrt{2}$
Multiply by $6$ : Multiply $\sqrt{2}$ by $6$ . $\sqrt{2} \times 6 = 6\sqrt{2}$
Multiply by $\sqrt{2}$ : Multiply $\sqrt{2}$ by $\sqrt{2}$ . $\sqrt{2} \times \sqrt{2} = 2$ This is because the square root of a number, when multiplied by itself, gives the original number.
Combine results: Combine the results from the previous steps to get the final expression. $6\sqrt{2} - 2$
Check for simplification: Check if the expression can be simplified further. $\newline$ Since $6\sqrt{2}$ and $2$ have no common factors and $\sqrt{2}$ is already in its simplest radical form, the expression cannot be simplified further.

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