Question

question

simplify: \\(\sqrt3{\frac{250m^5}{n^9}}\\).

provide your answer below:

Explanation:

Apply the quotient property of radicals

Using the Higher Roots knowledge point

$$ \sqrt[3]{\frac{250m^5}{n^9}} = \frac{\sqrt[3]{250m^5}}{\sqrt[3]{n^9}} $$

Simplify the denominator

Using the Higher Roots knowledge point

$$ \sqrt[3]{n^9} = n^{9/3} = n^3 $$

Factor the radicand in the numerator

Using the Simplifying Cube Roots knowledge point

$$
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$$

Simplify the numerator radical

Using the Simplifying Cube Roots knowledge point

$$ \sqrt[3]{250m^5} = \sqrt[3]{5^3 \cdot m^3 \cdot 2m^2} = 5m\sqrt[3]{2m^2} $$

Combine the simplified terms

Using the Simplifying Cube Roots and Higher Roots knowledge points

$$ \frac{5m\sqrt[3]{2m^2}}{n^3} $$

Answer:

Simplify: <blank>\(\frac{5m\sqrt[3]{2m^2}}{n^3}\)</blank>