Question

Simplify cube root of 8/27

Answer 1

Answer:

$\frac{2}{3}$

step by step explanation

$the \: above \: simply \: means \\ \: = \frac{ \sqrt[3]{8} }{ \sqrt[3]{27} } = \frac{2}{3}$

Answer 2

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$\sqrt[3]{ \frac{8}{27} }$

$=3 \times \frac{ \sqrt{ {2}^{2} \times 2 } }{ \sqrt{ {3}^{2} \times 2} }$

$= 3 \times \frac{ \sqrt{ {2}^{2} } \times \sqrt{2} }{ \sqrt{ {3}^{2} } \times \sqrt{3} }$

$= 3 \times \frac{ {2}^{ \frac{2}{2} } \times \sqrt{2} }{{3}^{ \frac{2}{2} } \times \sqrt{3} }$

$= 3 \times \frac{2 \times \sqrt{2} }{3 \times \sqrt{3} }$

$= \frac{3 \times 2 \times \sqrt{2} }{3 \times \sqrt{3} }$

$= \frac{2 \times \sqrt{2} }{ \sqrt{3} }$

$= \frac{2 \times \sqrt{6} }{ {3}^{ \frac{2}{2} } }$

$= \frac{2 \times \sqrt{6} }{3}$