Simplify. Assume f is greater than or equal to zero. sqrt 126f^9 ______

Factorize and Identify Perfect Squares: sqrt(126f^9) First, we need to factor the radicand into its prime factors and identify perfect squares. Prime factorization of 126 is 2 * 3^2 * 7, and f^9 can be written as (f^4)^2 * f. sqrt(126f^9) = sqrt(2 * 3^2 * 7 * (f^4)^2 * f)Group Identical Factors: sqrt(2 * 3^2 * 7 * (f^4)^2 * f) Now, group the identical factors and perfect squares. sqrt(2 * 3^2 * 7 * (f^4)^2 * f) = sqrt(3^2) * sqrt((f^4)^2) * sqrt(2 * 7 * f)Apply Product Property and Simplify: sqrt(3^2) * sqrt((f^4)^2) * sqrt(2 * 7 * f) Apply the product property of radicals and simplify the square roots of perfect squares. sqrt(3^2) * sqrt((f^4)^2) * sqrt(2 * 7 * f) = 3 * f^4 * sqrt(14f)Combine Simplified Terms: 3 * f^4 * sqrt(14f) Combine the simplified terms to get the final answer. 3f^4 * sqrt(14f)

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Simplify. Assume $f$ is greater than or equal to zero. $\newline$ $\sqrt{126f^9}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify. Assume

f

is greater than or equal to zero.

\newline

\sqrt{126f^9}

Factorize and Identify Perfect Squares: $\sqrt{126f^9}$ $\newline$ First, we need to factor the radicand into its prime factors and identify perfect squares. $\newline$ Prime factorization of $126$ is $2 \times 3^2 \times 7$ , and $f^9$ can be written as $(f^4)^2 \times f$ . $\newline$ $\sqrt{126f^9} = \sqrt{2 \times 3^2 \times 7 \times (f^4)^2 \times f}$
Group Identical Factors: $\sqrt{2 \times 3^2 \times 7 \times (f^4)^2 \times f}$ Now, group the identical factors and perfect squares. $\sqrt{2 \times 3^2 \times 7 \times (f^4)^2 \times f} = \sqrt{3^2} \times \sqrt{(f^4)^2} \times \sqrt{2 \times 7 \times f}$
Apply Product Property and Simplify: $\sqrt{3^2} \times \sqrt{(f^4)^2} \times \sqrt{2 \times 7 \times f}$ Apply the product property of radicals and simplify the square roots of perfect squares. $\sqrt{3^2} \times \sqrt{(f^4)^2} \times \sqrt{2 \times 7 \times f} = 3 \times f^4 \times \sqrt{14f}$
Combine Simplified Terms: $3 \cdot f^4 \cdot \sqrt{14f}$ $\newline$ Combine the simplified terms to get the final answer. $\newline$ $3f^4 \cdot \sqrt{14f}$