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

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Multiply radical expressions

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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, $\sqrt{270} \times \sqrt{3} = 9 \times \sqrt{10}$ .

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