Simplify. sqrt 350 ______

Find Prime Factors: sqrt(350) 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(350) = sqrt(2 * 5 * 5 * 7)Group and Combine: sqrt(2 * 5 * 5 * 7) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 5 * 5 * 7) = sqrt(2 * 5^2 * 7)Apply Product Property: sqrt(2 * 5^2 * 7) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2 * 5^2 * 7) = sqrt(5^2) * sqrt(2 * 7)Cancel Square Root: sqrt(350) = sqrt(5^2) * sqrt(2 * 7) Square and square root cancel each other out for the term sqrt(5^2). sqrt(5^2) * sqrt(2 * 7) = 5 * sqrt(14)

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Simplify. $\newline$ $\sqrt{350}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{350}

Find Prime Factors: $\sqrt{350}$ $\newline$ 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. $\newline$ $\sqrt{350} = \sqrt{2 \times 5 \times 5 \times 7}$
Group and Combine: $\sqrt{2 \times 5 \times 5 \times 7}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{2 \times 5 \times 5 \times 7} = \sqrt{2 \times 5^2 \times 7}$
Apply Product Property: $\sqrt{2 \times 5^2 \times 7}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2 \times 5^2 \times 7} = \sqrt{5^2} \times \sqrt{2 \times 7}$
Cancel Square Root: $\sqrt{350} = \sqrt{5^2} \times \sqrt{2 \times 7}$ $\newline$ Square and square root cancel each other out for the term $\sqrt{5^2}$ . $\newline$ $\sqrt{5^2} \times \sqrt{2 \times 7} = 5 \times \sqrt{14}$