Simplify. Assume x is greater than or equal to zero. sqrt 75x^9 ______

Factorization: Factor 75x^9 into its prime factors and perfect squares. 75 can be factored into 3 * 5 * 5, and x^9 is (x^4)^2 * x. So, we have: sqrt(75x^9) = sqrt(3 * 5^2 * (x^4)^2 * x)Separation: Separate the perfect squares from the non-perfect squares inside the radical. We can rewrite the expression as: sqrt(5^2 * (x^4)^2 * 3x)Square Roots: Take the square root of the perfect squares. The square root of 5^2 is 5, and the square root of (x^4)^2 is x^4. We then have: 5 * x^4 * sqrt(3x)Final Expression: Write the final simplified expression. The simplified form of the original expression is: 5x^4 * sqrt(3x)

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Simplify. Assume $x$ is greater than or equal to zero. $\newline$ $\sqrt{75x^9}$

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Algebra 1

Simplify radical expressions with variables

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Q. Simplify. Assume

x

is greater than or equal to zero.

\newline

\sqrt{75x^9}

Factorization: Factor $75x^9$ into its prime factors and perfect squares. $\newline$ $75$ can be factored into $3 \times 5 \times 5$ , and $x^9$ is $(x^4)^2 \times x$ . So, we have: $\newline$ $\sqrt{75x^9} = \sqrt{3 \times 5^2 \times (x^4)^2 \times x}$
Separation: Separate the perfect squares from the non-perfect squares inside the radical. $\newline$ We can rewrite the expression as: $\newline$ $\sqrt{5^2 \cdot (x^4)^2 \cdot 3x}$
Square Roots: Take the square root of the perfect squares. $\newline$ The square root of $5^2$ is $5$ , and the square root of $(x^4)^2$ is $x^4$ . We then have: $\newline$ $5 \times x^4 \times \sqrt{3x}$
Final Expression: Write the final simplified expression. $\newline$ The simplified form of the original expression is: $\newline$ $5x^4 \cdot \sqrt{3x}$