Multiply. Write your answer in simplest form. sqrt270*sqrt3

Find Prime Factorization: Find the prime factorization of sqrt(270) and sqrt(3). The prime factorization of 270 is 2 * 3^3 * 5, and the prime factorization of 3 is just 3. So, sqrt(270) * sqrt(3) can be expressed as sqrt(2 * 3^3 * 5) * sqrt(3).Combine Square Roots: Apply the multiplication property of square roots to combine them into one square root. So, sqrt(2 * 3^3 * 5) * sqrt(3) = sqrt(2 * 3^3 * 5 * 3).Combine Like Terms: Combine the like terms under the square root. So, sqrt(2 * 3^3 * 5 * 3) = sqrt(2 * 3^4 * 5).Pull Out Perfect Squares: Pull out the perfect square factors from the square root. So, sqrt(2 * 3^4 * 5) = 3^2 * sqrt(2 * 5).Simplify Final Result: Simplify 3^2 * sqrt(2 * 5). So, sqrt(270) * sqrt(3) = 9 * sqrt(10).

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{270} \times \sqrt{3}$

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{270} \times \sqrt{3}

Find Prime Factorization: Find the prime factorization of $\sqrt{270}$ and $\sqrt{3}$ . The prime factorization of $270$ is $2 \times 3^3 \times 5$ , and the prime factorization of $3$ is just $3$ . So, $\sqrt{270} \times \sqrt{3}$ can be expressed as $\sqrt{2 \times 3^3 \times 5} \times \sqrt{3}$ .
Combine Square Roots: Apply the multiplication property of square roots to combine them into one square root. So, $\sqrt{2 \times 3^3 \times 5} \times \sqrt{3} = \sqrt{2 \times 3^3 \times 5 \times 3}$ .
Combine Like Terms: Combine the like terms under the square root. So, $\sqrt{2 \times 3^3 \times 5 \times 3} = \sqrt{2 \times 3^4 \times 5}$ .
Pull Out Perfect Squares: Pull out the perfect square factors from the square root. So, $\sqrt{2 \times 3^4 \times 5} = 3^2 \times \sqrt{2 \times 5}$ .
Simplify Final Result: Simplify $3^2 \times \sqrt{2 \times 5}$ . So, $\sqrt{270} \times \sqrt{3} = 9 \times \sqrt{10}$ .