Simplify. sqrt 315 ______

Find Prime Factors: sqrt(315) Let's find the prime factors of the radicand (the number inside the square root). Prime factorization of a number is expressing it as the product of its prime factors. sqrt(315) = sqrt(3 * 3 * 5 * 7)Group and Combine Factors: sqrt(3 * 3 * 5 * 7) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(3 * 3 * 5 * 7) = sqrt(3^2 * 5 * 7)Apply Product Property: sqrt(3^2 * 5 * 7) Apply the product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(3^2 * 5 * 7) = sqrt(3^2) * sqrt(5) * sqrt(7)Simplify Perfect Square: sqrt(315) = sqrt(3^2) * sqrt(5) * sqrt(7) Simplify the square root of the perfect square. Square and square root cancel each other out. sqrt(3^2) * sqrt(5) * sqrt(7) = 3 * sqrt(5) * sqrt(7) = 3sqrt(35)

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Simplify. $\newline$ $\sqrt{315}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{315}

Find Prime Factors: $\sqrt{315}$ $\newline$ Let's find the prime factors of the radicand (the number inside the square root). $\newline$ Prime factorization of a number is expressing it as the product of its prime factors. $\newline$ $\sqrt{315} = \sqrt{3 \times 3 \times 5 \times 7}$
Group and Combine Factors: $\sqrt{3 \times 3 \times 5 \times 7}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{3 \times 3 \times 5 \times 7} = \sqrt{3^2 \times 5 \times 7}$
Apply Product Property: $\sqrt{3^2 \times 5 \times 7}$ $\newline$ Apply the product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{3^2 \times 5 \times 7} = \sqrt{3^2} \times \sqrt{5} \times \sqrt{7}$
Simplify Perfect Square: $\sqrt{315} = \sqrt{3^2} \times \sqrt{5} \times \sqrt{7}$ $\newline$ Simplify the square root of the perfect square. $\newline$ Square and square root cancel each other out. $\newline$ $\sqrt{3^2} \times \sqrt{5} \times \sqrt{7}$ $\newline$ $= 3 \times \sqrt{5} \times \sqrt{7}$ $\newline$ $= 3\sqrt{35}$