Simplify the Radical Expression ( square root of 3m)^2

${(\sqrt{3 m})}^{2}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 m}$ as ${(3 m)}^{\frac{1}{2}}$ .

${({(3 m)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(3 m)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

${(3 m)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 m)}^{\frac{2}{2}}$

Rewrite the expression.

${(3 m)}^{1}$

Simplify.

$3 m$