Solve (1/3-2/3)^2+sqrt[3]{4-7/8}-11/18

$$( \frac { 1 } { 3 } - \frac { 2 } { 3 } ) ^ { 2 } + \sqrt[ 3 ] { 4 - \frac { 7 } { 8 } } - \frac { 11 } { 18 }$$

Evaluate

$$\frac{5^{\frac{2}{3}}-1}{2}\approx 0.962008869$$

Solution Steps

Subtract \frac{2}{3} from \frac{1}{3} to get -\frac{1}{3}.

$$\left(-\frac{1}{3}\right)^{2}+\sqrt[3]{4-\frac{7}{8}}-\frac{11}{18}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}+\sqrt[3]{4-\frac{7}{8}}-\frac{11}{18}$$

Subtract \frac{7}{8} from 4 to get \frac{25}{8}.

$$\frac{1}{9}+\sqrt[3]{\frac{25}{8}}-\frac{11}{18}$$

Subtract \frac{11}{18} from \frac{1}{9} to get -\frac{1}{2}.

$$-\frac{1}{2}+\sqrt[3]{\frac{25}{8}}$$

Factor

$$\frac{5 ^ {\frac{2}{3}} - 1}{2} = 0.962008869106433$$