Question

Simplify cube root of 8/27

Answer 1

`\sqrt[3]{ (8)/(27) }`

`=3 * \frac{ \sqrt{ {2}^(2) * 2 } }{ \sqrt{ {3}^(2) * 2} }`

`= 3 * \frac{ \sqrt{ {2}^(2) } * √(2) }{ \sqrt{ {3}^(2) } * √(3) }`

`= 3 * \frac{ {2}^{ (2)/(2) } * √(2) }{{3}^{ (2)/(2) } * √(3) }`

`= 3 * (2 * √(2) )/(3 * √(3) )`

`= (3 * 2 * √(2) )/(3 * √(3) )`

`= (2 * √(2) )/( √(3) )`

`= \frac{2 * √(6) }{ {3}^{ (2)/(2) } }`

`= (2 * √(6) )/(3)`

Answer 2

`(2)/(3)`

step by step explanation

`the \: above \: simply \: means \\ \: = \frac{ \sqrt[3]{8} }{ \sqrt[3]{27} } = (2)/(3)`