Multiply. Write your answer in simplest form. sqrt 273 * sqrt 42 ______

Find prime factorization: Find the prime factorization of the numbers under the square roots to simplify the expression. The prime factorization of 273 is 3 * 7 * 13, and the prime factorization of 42 is 2 * 3 * 7. So, sqrt(273) * sqrt(42) can be expressed as sqrt(3 * 7 * 13) * sqrt(2 * 3 * 7).Combine square roots: Apply the multiplication property of square roots to combine the two square roots into one. This gives us sqrt(3 * 7 * 13) * sqrt(2 * 3 * 7) = sqrt(3 * 7 * 13 * 2 * 3 * 7).Group perfect square factors: Group the perfect square factors together within the square root. We have sqrt(3 * 7 * 13 * 2 * 3 * 7) = sqrt(2 * 13 * 3^2 * 7^2).Extract perfect square factors: Extract the perfect square factors from the square root. The square root of a perfect square is the base of that square. So, sqrt(2 * 13 * 3^2 * 7^2) = 3 * 7 * sqrt(13 * 2) because 3^2 and 7^2 are perfect squares.Simplify the expression: Simplify the expression by multiplying the numbers outside the square root and keeping the square root as is. So, 3 * 7 * sqrt(13 * 2) simplifies to 21 * sqrt(26).

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{273} \times \sqrt{42}$ $\newline$ ______

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{273} \times \sqrt{42}

\newline

______

Find prime factorization: Find the prime factorization of the numbers under the square roots to simplify the expression. The prime factorization of $273$ is $3 \times 7 \times 13$ , and the prime factorization of $42$ is $2 \times 3 \times 7$ . So, $\sqrt{273} \times \sqrt{42}$ can be expressed as $\sqrt{3 \times 7 \times 13} \times \sqrt{2 \times 3 \times 7}$ .
Combine square roots: Apply the multiplication property of square roots to combine the two square roots into one. This gives us $\sqrt{3 \times 7 \times 13} \times \sqrt{2 \times 3 \times 7} = \sqrt{3 \times 7 \times 13 \times 2 \times 3 \times 7}$ .
Group perfect square factors: Group the perfect square factors together within the square root. We have $\sqrt{3 \times 7 \times 13 \times 2 \times 3 \times 7} = \sqrt{2 \times 13 \times 3^2 \times 7^2}$ .
Extract perfect square factors: Extract the perfect square factors from the square root. The square root of a perfect square is the base of that square. So, $\sqrt{2 \times 13 \times 3^2 \times 7^2} = 3 \times 7 \times \sqrt{13 \times 2}$ because $3^2$ and $7^2$ are perfect squares.
Simplify the expression: Simplify the expression by multiplying the numbers outside the square root and keeping the square root as is. So, $3 \times 7 \times \sqrt{13 \times 2}$ simplifies to $21 \times \sqrt{26}$ .