Simplify. sqrt 147 ______

Find Prime Factors: sqrt(147) 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(147) = sqrt(3 * 7 * 7)Group and Combine Factors: sqrt(3 * 7 * 7) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(3 * 7 * 7) = sqrt(3 * 7^2)Apply Product Property: sqrt(3 * 7^2) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(3 * 7^2) = sqrt(3) * sqrt(7^2)Simplify the Expression: sqrt(147) = sqrt(3) * sqrt(7^2) What is the simplest form of sqrt(147)? Square and square root cancel each other out. sqrt(3) * sqrt(7^2) = sqrt(3) * 7 = 7sqrt(3)

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Simplify. $\newline$ $\sqrt{147}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{147}

Find Prime Factors: $\sqrt{147}$ $\newline$ 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. $\newline$ $\sqrt{147} = \sqrt{3 \times 7 \times 7}$
Group and Combine Factors: $\sqrt{3 \times 7 \times 7}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{3 \times 7^2}$
Apply Product Property: $\sqrt{3 \times 7^2}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{3 \times 7^2} = \sqrt{3} \times \sqrt{7^2}$
Simplify the Expression: $\sqrt{147} = \sqrt{3} \times \sqrt{7^2}$ $\newline$ What is the simplest form of $\sqrt{147}$ ? $\newline$ Square and square root cancel each other out. $\newline$ $\sqrt{3} \times \sqrt{7^2} = \sqrt{3} \times 7$ $\newline$ $= 7\sqrt{3}$