Solve sqrt[3]{9(1-1/3)^2-3/2+frac{1{2}}}

$$\sqrt[ 3 ] { \frac { 9 ( 1 - \frac { 1 } { 3 } ) ^ { 2 } - 3 } { 2 + \frac { 1 } { 2 } } }$$

Evaluate

$$\frac{\sqrt[3]{2}\times 5^{\frac{2}{3}}}{5}\approx 0.7368063$$

Solution Steps

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

$$\sqrt[3]{\frac{9\times \left(\frac{2}{3}\right)^{2}-3}{2+\frac{1}{2}}}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\sqrt[3]{\frac{9\times \frac{4}{9}-3}{2+\frac{1}{2}}}$$

Multiply 9 and \frac{4}{9} to get 4.

$$\sqrt[3]{\frac{4-3}{2+\frac{1}{2}}}$$

Subtract 3 from 4 to get 1.

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

Add 2 and \frac{1}{2} to get \frac{5}{2}.

$$\sqrt[3]{\frac{1}{\frac{5}{2}}}$$

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

$$\sqrt[3]{1\times \frac{2}{5}}$$

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

$$\sqrt[3]{\frac{2}{5}}$$