Question

How to divide and simplify this radical expression

Answer 1

`(2x)/(5)\sqrt[3]{50x^2}`

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\frac{\sqrt[3]{16x^8y^2}}{\sqrt[3]{5x^3y^2}}=\sqrt[3]{(16x^8y^2)/(5x^3y^2)}=\sqrt[3]{(16x^5)/(5)}=\sqrt[3]{((2x)^3\cdot2\cdot5^2x^2)/(5^3)}\\\\=\boxed{(2x)/(5)\sqrt[3]{50x^2}}`