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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{14}\times\sqrt{308}$

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Multiply radical expressions

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{14}\times\sqrt{308}

Find Prime Factorization: Find the prime factorization of $\sqrt{14}$ and $\sqrt{308}$ . The prime factorization of $14$ is $2 \times 7$ , and the prime factorization of $308$ is $2 \times 2 \times 7 \times 11$ . So, $\sqrt{14} \times \sqrt{308}$ can be expressed as $\sqrt{2 \times 7} \times \sqrt{2 \times 2 \times 7 \times 11}$ .
Combine Square Roots: Apply the multiplication property of square roots to combine them into one square root. So, $\sqrt{2 \times 7} \times \sqrt{2 \times 2 \times 7 \times 11} = \sqrt{2 \times 7 \times 2 \times 2 \times 7 \times 11}$ .
Group Perfect Square Factors: Group the perfect square factors inside the square root. So, $\sqrt{2 \times 7 \times 2 \times 2 \times 7 \times 11} = \sqrt{2^2 \times 7^2 \times 2 \times 11}$ .
Pull Out Factors: Pull out the perfect square factors from the square root. So, $\sqrt{2^2 \times 7^2 \times 2 \times 11} = 2 \times 7 \times \sqrt{2 \times 11}$ .
Simplify Expression: Simplify the expression. So, $\sqrt{14} \times \sqrt{308} = 2 \times 7 \times \sqrt{2 \times 11} = 14 \times \sqrt{22}.$

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