Calculate the product and express in reduced form. sqrt45*sqrt5

Find Prime Factorization: Find the prime factorization of sqrt(45) and sqrt(5). The prime factorization of 45 is 3 * 3 * 5, and the prime factorization of 5 is just 5. So, sqrt(45) * sqrt(5) can be expressed as sqrt(3 * 3 * 5) * sqrt(5).Combine Square Roots: Apply the multiplication property of square roots to combine them. So, sqrt(3 * 3 * 5) * sqrt(5) = sqrt(3 * 3 * 5 * 5).Group Perfect Squares: Group the perfect square factors in sqrt(3 * 3 * 5 * 5). So, sqrt(3 * 3 * 5 * 5) = sqrt(3^2 * 5^2).Pull Out Base: Pull out the base of perfect square factors from sqrt(3^2 * 5^2). So, sqrt(3^2 * 5^2) = 3 * 5.Simplify Result: Simplify 3 * 5. So, sqrt(45) * sqrt(5) = 3 * 5 = 15.

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Calculate the product and express in reduced form. $\newline$ $\sqrt{45}\times\sqrt{5}$

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Algebra 2

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Q. Calculate the product and express in reduced form.

\newline

\sqrt{45}\times\sqrt{5}

Find Prime Factorization: Find the prime factorization of $\sqrt{45}$ and $\sqrt{5}$ . The prime factorization of $45$ is $3 \times 3 \times 5$ , and the prime factorization of $5$ is just $5$ . So, $\sqrt{45} \times \sqrt{5}$ can be expressed as $\sqrt{3 \times 3 \times 5} \times \sqrt{5}$ .
Combine Square Roots: Apply the multiplication property of square roots to combine them. So, $\sqrt{3 \times 3 \times 5} \times \sqrt{5} = \sqrt{3 \times 3 \times 5 \times 5}$ .
Group Perfect Squares: Group the perfect square factors in $\sqrt{3 \times 3 \times 5 \times 5}$ . So, $\sqrt{3 \times 3 \times 5 \times 5} = \sqrt{3^2 \times 5^2}$ .
Pull Out Base: Pull out the base of perfect square factors from $\sqrt{3^2 \times 5^2}$ . So, $\sqrt{3^2 \times 5^2} = 3 \times 5$ .
Simplify Result: Simplify $3 \times 5$ . So, $\sqrt{45} \times \sqrt{5} = 3 \times 5 = 15$ .