Solve sqrt[3]{164/125}-sqrt[3]{8}+sqrt{1/100}-(-2)^3*sqrt[3]{0.064}

$$\sqrt[ 3 ] { \frac { 164 } { 125 } } - \sqrt[ 3 ] { 8 } + \sqrt { \frac { 1 } { 100 } } - ( - 2 ) ^ { 3 } \times \sqrt[ 3 ] { 0.064 }$$

Evaluate

$$\frac{\sqrt[3]{164}}{5}+1.3\approx 2.394740735$$

Solution Steps

Calculate \sqrt[3]{8} and get 2.

$$\sqrt[3]{\frac{164}{125}}-2+\sqrt{\frac{1}{100}}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Rewrite the square root of the division \frac{1}{100} as the division of square roots \frac{\sqrt{1}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\sqrt[3]{\frac{164}{125}}-2+\frac{1}{10}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Add -2 and \frac{1}{10} to get -\frac{19}{10}.

$$\sqrt[3]{\frac{164}{125}}-\frac{19}{10}-\left(-2\right)^{3}\sqrt[3]{0.064}$$

Calculate -2 to the power of 3 and get -8.

$$\sqrt[3]{\frac{164}{125}}-\frac{19}{10}-\left(-8\sqrt[3]{0.064}\right)$$

Calculate \sqrt[3]{0.064} and get \frac{2}{5}.

$$\sqrt[3]{\frac{164}{125}}-\frac{19}{10}-\left(-8\times \frac{2}{5}\right)$$

Multiply -8 and \frac{2}{5} to get -\frac{16}{5}.

$$\sqrt[3]{\frac{164}{125}}-\frac{19}{10}-\left(-\frac{16}{5}\right)$$

The opposite of -\frac{16}{5} is \frac{16}{5}.

$$\sqrt[3]{\frac{164}{125}}-\frac{19}{10}+\frac{16}{5}$$

Add -\frac{19}{10} and \frac{16}{5} to get \frac{13}{10}.

$$\sqrt[3]{\frac{164}{125}}+\frac{13}{10}$$