Find the value of \(\left(\sqrt[3]{\frac{125}{27}}-\sqrt[3]{\frac{512}{729}}\right)\div\sqrt[3]{\frac{64}{5832}}\):
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3.5
The cube root of a fraction is the cube root of the numerator over the cube root of the denominator, and every number here is a perfect cube.
\(\displaystyle \sqrt[3]{\frac{125}{27}}=\frac{5}{3}\) and \(\displaystyle \sqrt[3]{\frac{512}{729}}=\frac{8}{9}\)
\(\displaystyle \frac{5}{3}-\frac{8}{9}=\frac{15-8}{9}=\frac{7}{9}\)
\(\displaystyle \sqrt[3]{\frac{64}{5832}}=\frac{4}{18}=\frac{2}{9}\) (as \(18^{3}=5832\))
\(\displaystyle \frac{7}{9}\div\frac{2}{9}=\frac{7}{2}=3.5\)