Solve for: cube root of (8x^2)/(y)

Expression: $\sqrt[3]{\frac{ 8{x}^{2} }{ y }}$

To take a root of a fraction, take the root of the numerator and denominator separately

$\frac{ \sqrt[3]{8{x}^{2}} }{ \sqrt[3]{y} }$

Simplify the radical expression

$\frac{ 2\sqrt[3]{{x}^{2}} }{ \sqrt[3]{y} }$

Multiply the fraction by $\frac{ \sqrt[3]{{y}^{2}} }{ \sqrt[3]{{y}^{2}} }$

$\frac{ 2\sqrt[3]{{x}^{2}} }{ \sqrt[3]{y} } \times \frac{ \sqrt[3]{{y}^{2}} }{ \sqrt[3]{{y}^{2}} }$

To multiply the fractions, multiply the numerators and denominators separately

$\frac{ 2\sqrt[3]{{x}^{2}}\sqrt[3]{{y}^{2}} }{ \sqrt[3]{y}\sqrt[3]{{y}^{2}} }$

Calculate the product

$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ \sqrt[3]{y}\sqrt[3]{{y}^{2}} }$

The product of roots with the same index is equal to the root of the product

$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ \sqrt[3]{y \times {y}^{2}} }$

Calculate the product

$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ \sqrt[3]{{y}^{3}} }$

Reduce the index of the radical and exponent with $3$

$\frac{ 2\sqrt[3]{{x}^{2}{y}^{2}} }{ y }$

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