Solve sqrt{2/3+(1+1/2)*[(3/2)^2-(1-2/5):(frac{8}{5}:11+frac{4}{33})]^0,01}=

$$\sqrt { \frac { 2 } { 3 } + ( 1 + \frac { 1 } { 2 } ) \cdot [ ( \frac { 3 } { 2 } ) ^ { 2 } - ( 1 - \frac { 2 } { 5 } ) : ( \frac { 8 } { 5 } : 11 + \frac { 4 } { 33 } ) ] ^ { 0,01 } } =$$

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Solution Steps

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\left(\frac{3}{2}\right)^{2}-\frac{1-\frac{2}{5}}{\frac{\frac{8}{5}}{11}+\frac{4}{33}}\right)^{0,01}}$$

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

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\frac{9}{4}-\frac{1-\frac{2}{5}}{\frac{\frac{8}{5}}{11}+\frac{4}{33}}\right)^{0,01}}$$

Subtract \frac{2}{5} from 1 to get \frac{3}{5}.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\frac{9}{4}-\frac{\frac{3}{5}}{\frac{\frac{8}{5}}{11}+\frac{4}{33}}\right)^{0,01}}$$

Express \frac{\frac{8}{5}}{11} as a single fraction.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\frac{9}{4}-\frac{\frac{3}{5}}{\frac{8}{5\times 11}+\frac{4}{33}}\right)^{0,01}}$$

Multiply 5 and 11 to get 55.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\frac{9}{4}-\frac{\frac{3}{5}}{\frac{8}{55}+\frac{4}{33}}\right)^{0,01}}$$

Add \frac{8}{55} and \frac{4}{33} to get \frac{4}{15}.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\frac{9}{4}-\frac{\frac{3}{5}}{\frac{4}{15}}\right)^{0,01}}$$

Divide \frac{3}{5} by \frac{4}{15} by multiplying \frac{3}{5} by the reciprocal of \frac{4}{15}.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\frac{9}{4}-\frac{3}{5}\times \frac{15}{4}\right)^{0,01}}$$

Multiply \frac{3}{5} and \frac{15}{4} to get \frac{9}{4}.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\left(\frac{9}{4}-\frac{9}{4}\right)^{0,01}}$$

Subtract \frac{9}{4} from \frac{9}{4} to get 0.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\times 0^{0,01}}$$

Calculate 0 to the power of 0,01 and get 0.

$$\sqrt{\frac{2}{3}+\frac{3}{2}\times 0}$$

Multiply \frac{3}{2} and 0 to get 0.

$$\sqrt{\frac{2}{3}+0}$$

Add \frac{2}{3} and 0 to get \frac{2}{3}.

$$\sqrt{\frac{2}{3}}$$

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$\frac{\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3}$$