Simplify. Assume f is greater than or equal to zero. sqrt 250f ______

Find Prime Factors: sqrt(250f) Let's start by finding the prime factors of the number 250. Prime factorization of a number is the expression of the number as a product of its prime factors. sqrt(250f) = sqrt(2 * 5 * 5 * 5 * f)Group and Combine Factors: sqrt(2 * 5 * 5 * 5 * f) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 5 * 5 * 5 * f) = sqrt(2 * 5^3 * f)Apply Product Property: sqrt(2 * 5^3 * f) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2 * 5^3 * f) = sqrt(2) * sqrt(5^3) * sqrt(f)Simplify Square Roots: sqrt(2) * sqrt(5^3) * sqrt(f) Since sqrt(5^3) can be simplified to 5 * sqrt(5) because 5^2 = 25 and sqrt(25) = 5, we can rewrite the expression as: sqrt(2) * 5 * sqrt(5) * sqrt(f)Combine Square Roots: sqrt(2) * 5 * sqrt(5) * sqrt(f) Now, we can combine the square roots of 5 and f. sqrt(2) * 5 * sqrt(5 * f)Final Simplified Form: sqrt(2) * 5 * sqrt(5 * f) The final simplified form is: 5 * sqrt(2) * sqrt(5f) 5 * sqrt(10f)

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Simplify. Assume $f$ is greater than or equal to zero. $\newline$ $\sqrt{250f}$

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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{250f}

Find Prime Factors: $\sqrt{250f}$ $\newline$ Let's start by finding the prime factors of the number $250$ . $\newline$ Prime factorization of a number is the expression of the number as a product of its prime factors. $\newline$ $\sqrt{250f} = \sqrt{2 \times 5 \times 5 \times 5 \times f}$
Group and Combine Factors: $\sqrt{2 \times 5 \times 5 \times 5 \times f}$ Now, group the identical factors. Combine the identical factors by using the exponents. $\sqrt{2 \times 5 \times 5 \times 5 \times f} = \sqrt{2 \times 5^3 \times f}$
Apply Product Property: $\sqrt{2 \times 5^3 \times f}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2 \times 5^3 \times f} = \sqrt{2} \times \sqrt{5^3} \times \sqrt{f}$
Simplify Square Roots: $\sqrt{2} \times \sqrt{5^3} \times \sqrt{f}$ $\newline$ Since $\sqrt{5^3}$ can be simplified to $5 \times \sqrt{5}$ because $5^2 = 25$ and $\sqrt{25} = 5$ , we can rewrite the expression as: $\newline$ $\sqrt{2} \times 5 \times \sqrt{5} \times \sqrt{f}$
Combine Square Roots: $\sqrt{2} \times 5 \times \sqrt{5} \times \sqrt{f}$ $\newline$ Now, we can combine the square roots of $5$ and f. $\newline$ $\sqrt{2} \times 5 \times \sqrt{5 \times f}$
Final Simplified Form: $\sqrt{2} \times 5 \times \sqrt{5 \times f}$ $\newline$ The final simplified form is: $\newline$ $5 \times \sqrt{2} \times \sqrt{5f}$ $\newline$ $5 \times \sqrt{10f}$