Solve (2/3-1/2)^2*1/27+sqrt{1/20+frac{11}{100}}=

$$( \frac { 2 } { 3 } - \frac { 1 } { 2 } ) ^ { 2 } \cdot \frac { 1 } { 27 } + \sqrt { \frac { 1 } { 20 } + \frac { 11 } { 100 } } =$$

Evaluate

$$\frac{1949}{4860}\approx 0.401028807$$

Solution Steps

Subtract \frac{1}{2} from \frac{2}{3} to get \frac{1}{6}.

$$\left(\frac{1}{6}\right)^{2}\times \frac{1}{27}+\sqrt{\frac{1}{20}+\frac{11}{100}}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{1}{36}\times \frac{1}{27}+\sqrt{\frac{1}{20}+\frac{11}{100}}$$

Multiply \frac{1}{36} and \frac{1}{27} to get \frac{1}{972}.

$$\frac{1}{972}+\sqrt{\frac{1}{20}+\frac{11}{100}}$$

Add \frac{1}{20} and \frac{11}{100} to get \frac{4}{25}.

$$\frac{1}{972}+\sqrt{\frac{4}{25}}$$

Rewrite the square root of the division \frac{4}{25} as the division of square roots \frac{\sqrt{4}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{1}{972}+\frac{2}{5}$$

Add \frac{1}{972} and \frac{2}{5} to get \frac{1949}{4860}.

$$\frac{1949}{4860}$$

Factor

$$\frac{1949}{2 ^ {2} \cdot 3 ^ {5} \cdot 5} = 0.40102880658436213$$