Question

How to divide and simplify this radical expression

Answer 1

Answer:

  $\dfrac{2x}{5}\sqrt[3]{50x^2}$

Step-by-step explanation:

Since the root indices are the same, the fraction can be combined under one radical. Then you want to do two things:

• factor out perfect cubes
• make the denominator a perfect cube (so it can be factored out)

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  $\displaystyle\dfrac{\sqrt[3]{16x^8y^2}}{\sqrt[3]{5x^3y^2}}=\sqrt[3]{\dfrac{16x^8y^2}{5x^3y^2}}=\sqrt[3]{\dfrac{16x^5}{5}}=\sqrt[3]{\dfrac{(2x)^3\cdot2\cdot5^2x^2}{5^3}}\\\\=\boxed{\dfrac{2x}{5}\sqrt[3]{50x^2}}$