Simplify. Assume x is greater than or equal to zero. sqrt 45x^9 ______

Factorization: Factor 45x^9 into its prime factors and perfect squares. 45 can be factored into 9 * 5, where 9 is a perfect square. The x^9 term can be written as (x^4)^2 * x, where (x^4)^2 is a perfect square. So, 45x^9 = 9 * 5 * (x^4)^2 * x.Rewrite Expression: Rewrite the square root of the expression using the factorization. sqrt(45x^9) = sqrt(9 * 5 * (x^4)^2 * x).Simplify Square Root: Simplify the square root by taking out the perfect squares. sqrt(9 * 5 * (x^4)^2 * x) = sqrt(9) * sqrt((x^4)^2) * sqrt(5x). This simplifies to 3 * x^4 * sqrt(5x).Combine Terms: Combine the simplified terms outside of the square root. The final simplified expression is 3x^4 * sqrt(5x).

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Simplify. Assume $x$ is greater than or equal to zero. $\newline$ $\sqrt{45x^9}$

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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{45x^9}

Factorization: Factor $45x^9$ into its prime factors and perfect squares. $\newline$ $45$ can be factored into $9 \times 5$ , where $9$ is a perfect square. The $x^9$ term can be written as $(x^4)^2 \times x$ , where $(x^4)^2$ is a perfect square. $\newline$ So, $45x^9 = 9 \times 5 \times (x^4)^2 \times x$ .
Rewrite Expression: Rewrite the square root of the expression using the factorization. $\sqrt{45x^9} = \sqrt{9 \times 5 \times (x^4)^2 \times x}$ .
Simplify Square Root: Simplify the square root by taking out the perfect squares. $\sqrt{9 \times 5 \times (x^4)^2 \times x} = \sqrt{9} \times \sqrt{(x^4)^2} \times \sqrt{5x}$ . This simplifies to $3 \times x^4 \times \sqrt{5x}$ .
Combine Terms: Combine the simplified terms outside of the square root. The final simplified expression is $3x^4 \cdot \sqrt{5x}$ .