Solve sqrt[3]{0.729*0.064}-sqrt[3]{0.512/64}

$$\sqrt[ 3 ] { 0.729 \times 0.064 } - \sqrt[ 3 ] { \frac { 0.512 } { 64 } }$$

Evaluate

$$0.16$$

Solution Steps

Multiply 0.729 and 0.064 to get 0.046656.

$$\sqrt[3]{0.046656}-\sqrt[3]{\frac{0.512}{64}}$$

Calculate \sqrt[3]{0.046656} and get \frac{9}{25}.

$$\frac{9}{25}-\sqrt[3]{\frac{0.512}{64}}$$

Expand \frac{0.512}{64} by multiplying both numerator and the denominator by 1000.

$$\frac{9}{25}-\sqrt[3]{\frac{512}{64000}}$$

Reduce the fraction \frac{512}{64000} to lowest terms by extracting and canceling out 512.

$$\frac{9}{25}-\sqrt[3]{\frac{1}{125}}$$

Calculate \sqrt[3]{\frac{1}{125}} and get \frac{1}{5}.

$$\frac{9}{25}-\frac{1}{5}$$

Subtract \frac{1}{5} from \frac{9}{25} to get \frac{4}{25}.

$$\frac{4}{25}$$

Factor

$$\frac{2 ^ {2}}{5 ^ {2}} = 0.16$$