Simplify. Assume m is greater than or equal to zero. sqrt 20m^9 ______

Factor Perfect Squares: Factor the expression inside the square root to identify perfect squares. The complete factorization of 20m^9 is 2*2*5*m*m*m*m*m*m*m*m*m.Group Factors: Group the factors into perfect squares inside the radical. sqrt(20m^9) becomes sqrt(2*2*5*m^8*m), which can be rearranged as sqrt(4*5*m^8*m).Simplify Perfect Squares: Simplify the square root of the perfect squares. Since sqrt(4) is 2 and sqrt(m^8) is m^4, we can take these outside the square root. This gives us 2*m^4*sqrt(5m).Write Final Expression: Write the final simplified expression. The simplified form of sqrt(20m^9) is 2m^4*sqrt(5m).

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Simplify. Assume $m$ is greater than or equal to zero. $\newline$ $\sqrt{20m^9}$

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Algebra 1

Simplify radical expressions with variables

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Q. Simplify. Assume

m

is greater than or equal to zero.

\newline

\sqrt{20m^9}

Factor Perfect Squares: Factor the expression inside the square root to identify perfect squares. $\newline$ The complete factorization of $20m^9$ is $2\ast2\ast5\ast m\ast m\ast m\ast m\ast m\ast m\ast m\ast m$ .
Group Factors: Group the factors into perfect squares inside the radical. $\sqrt{20m^9}$ becomes $\sqrt{2\times 2\times 5\times m^8\times m}$ , which can be rearranged as $\sqrt{4\times 5\times m^8\times m}$ .
Simplify Perfect Squares: Simplify the square root of the perfect squares. $\newline$ Since $\sqrt{4}$ is $2$ and $\sqrt{m^8}$ is $m^4$ , we can take these outside the square root. $\newline$ This gives us $2\cdot m^4\cdot\sqrt{5m}$ .
Write Final Expression: Write the final simplified expression. $\newline$ The simplified form of $\sqrt{20m^9}$ is $2m^4\sqrt{5m}$ .