Multiply. Write your answer in simplest form. sqrt66*sqrt39

Find Prime Factorization: Find the prime factorization of sqrt(66) and sqrt(39). The prime factorization of 66 is 2 * 3 * 11, and the prime factorization of 39 is 3 * 13. So, sqrt(66) * sqrt(39) can be expressed as sqrt(2 * 3 * 11) * sqrt(3 * 13).Apply Multiplication Property: Apply the multiplication property of square roots: sqrt(2 * 3 * 11) * sqrt(3 * 13) = sqrt(2 * 3 * 11 * 3 * 13).Group Perfect Square Factors: Group the perfect square factors: sqrt(2 * 3 * 11 * 3 * 13) = sqrt(2 * 3^2 * 11 * 13).Pull Out Base: Pull out the base of the perfect square factor: sqrt(2 * 3^2 * 11 * 13) = 3 * sqrt(2 * 11 * 13).Simplify Expression: Simplify 3 * sqrt(2 * 11 * 13): sqrt(66) * sqrt(39) = 3 * sqrt(2 * 11 * 13) = 3 * sqrt(286).

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{66} \times \sqrt{39}$

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{66} \times \sqrt{39}

Find Prime Factorization: Find the prime factorization of $\sqrt{66}$ and $\sqrt{39}$ . The prime factorization of $66$ is $2 \times 3 \times 11$ , and the prime factorization of $39$ is $3 \times 13$ . So, $\sqrt{66} \times \sqrt{39}$ can be expressed as $\sqrt{2 \times 3 \times 11} \times \sqrt{3 \times 13}$ .
Apply Multiplication Property: Apply the multiplication property of square roots: $\sqrt{2 \times 3 \times 11} \times \sqrt{3 \times 13} = \sqrt{2 \times 3 \times 11 \times 3 \times 13}$ .
Group Perfect Square Factors: Group the perfect square factors: $\sqrt{2 \times 3 \times 11 \times 3 \times 13} = \sqrt{2 \times 3^2 \times 11 \times 13}$ .
Pull Out Base: Pull out the base of the perfect square factor: $\sqrt{2 \times 3^2 \times 11 \times 13} = 3 \times \sqrt{2 \times 11 \times 13}$ .
Simplify Expression: Simplify $3 \times \sqrt{2 \times 11 \times 13}$ : $\sqrt{66} \times \sqrt{39} = 3 \times \sqrt{2 \times 11 \times 13} = 3 \times \sqrt{286}$ .