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

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Simplify radical expressions with variables

Full solution

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 $2m^4\sqrt{5m}$ .

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