Simplify. Assume f is greater than or equal to zero. sqrt 50f^3 ______

Prime Factorization: sqrt(50f^3) Let's do the prime factors of the radicand for the numerical part and express the variable part with exponents. Prime factorization of 50 is 2 * 5 * 5, and f^3 is already expressed with an exponent. sqrt(50f^3) = sqrt(2 * 5^2 * f^3)Group Identical Factors: sqrt(2 * 5^2 * f^3) Now, group the identical factors and express the variable part in pairs. Combine the identical factors by using the exponents. sqrt(2 * 5^2 * f^3) = sqrt(5^2) * sqrt(2) * sqrt(f^2) * sqrt(f)Product Property of Radicals: sqrt(5^2) * sqrt(2) * sqrt(f^2) * sqrt(f) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(5^2) * sqrt(2) * sqrt(f^2) * sqrt(f) = 5 * sqrt(2) * f * sqrt(f)Combine Numerical and Variable Parts: sqrt(50f^3) = 5 * sqrt(2) * f * sqrt(f) What is the simplest form of sqrt(50f^3)? Combine the numerical and variable parts that are outside the square root. 5 * f * sqrt(2) * sqrt(f) = 5f * sqrt(2f)

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Simplify. Assume $f$ is greater than or equal to zero. $\newline$ $\sqrt{50f^3}$

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Algebra 1

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Q. Simplify. Assume

f

is greater than or equal to zero.

\newline

\sqrt{50f^3}

Prime Factorization: $\sqrt{50f^3}$ $\newline$ Let's do the prime factors of the radicand for the numerical part and express the variable part with exponents. $\newline$ Prime factorization of $50$ is $2 \times 5 \times 5$ , and $f^3$ is already expressed with an exponent. $\newline$ $\sqrt{50f^3} = \sqrt{2 \times 5^2 \times f^3}$
Group Identical Factors: $\sqrt{2 \times 5^2 \times f^3}$ $\newline$ Now, group the identical factors and express the variable part in pairs. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{2 \times 5^2 \times f^3} = \sqrt{5^2} \times \sqrt{2} \times \sqrt{f^2} \times \sqrt{f}$
Product Property of Radicals: $\sqrt{5^2} \cdot \sqrt{2} \cdot \sqrt{f^2} \cdot \sqrt{f}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ $\newline$ $\sqrt{5^2} \cdot \sqrt{2} \cdot \sqrt{f^2} \cdot \sqrt{f} = 5 \cdot \sqrt{2} \cdot f \cdot \sqrt{f}$
Combine Numerical and Variable Parts: $\sqrt{50f^3} = 5 \times \sqrt{2} \times f \times \sqrt{f}$ What is the simplest form of $\sqrt{50f^3}$ ? Combine the numerical and variable parts that are outside the square root. $5 \times f \times \sqrt{2} \times \sqrt{f}$ = $5f \times \sqrt{2f}$