Solve sqrt{4/5*[(11/14+1/4)-(3/14+frac{5}{4}-frac{3}{7})]^3+{(frac{3}{2}+frac{3}{4})*(frac{9}{21}*(frac{11}{15}+frac{1}{5}))*frac{5}{3}}*frac{3}{2}}

$$\sqrt { \frac { 4 } { 5 } \times [ ( \frac { 11 } { 14 } + \frac { 1 } { 4 } ) - ( \frac { 3 } { 14 } + \frac { 5 } { 4 } - \frac { 3 } { 7 } ) ] ^ { 3 } + \{ ( \frac { 3 } { 2 } + \frac { 3 } { 4 } ) \times ( \frac { 9 } { 21 } \times ( \frac { 11 } { 15 } + \frac { 1 } { 5 } ) ) \times \frac { 5 } { 3 } \} \cdot \frac { 3 } { 2 } }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Add \frac{11}{14} and \frac{1}{4} to get \frac{29}{28}.

$$\sqrt{\frac{4}{5}\left(\frac{29}{28}-\left(\frac{3}{14}+\frac{5}{4}-\frac{3}{7}\right)\right)^{3}+\left(\frac{3}{2}+\frac{3}{4}\right)\times \frac{9}{21}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Add \frac{3}{14} and \frac{5}{4} to get \frac{41}{28}.

$$\sqrt{\frac{4}{5}\left(\frac{29}{28}-\left(\frac{41}{28}-\frac{3}{7}\right)\right)^{3}+\left(\frac{3}{2}+\frac{3}{4}\right)\times \frac{9}{21}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Subtract \frac{3}{7} from \frac{41}{28} to get \frac{29}{28}.

$$\sqrt{\frac{4}{5}\left(\frac{29}{28}-\frac{29}{28}\right)^{3}+\left(\frac{3}{2}+\frac{3}{4}\right)\times \frac{9}{21}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Subtract \frac{29}{28} from \frac{29}{28} to get 0.

$$\sqrt{\frac{4}{5}\times 0^{3}+\left(\frac{3}{2}+\frac{3}{4}\right)\times \frac{9}{21}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Calculate 0 to the power of 3 and get 0.

$$\sqrt{\frac{4}{5}\times 0+\left(\frac{3}{2}+\frac{3}{4}\right)\times \frac{9}{21}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Multiply \frac{4}{5} and 0 to get 0.

$$\sqrt{0+\left(\frac{3}{2}+\frac{3}{4}\right)\times \frac{9}{21}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Add \frac{3}{2} and \frac{3}{4} to get \frac{9}{4}.

$$\sqrt{0+\frac{9}{4}\times \frac{9}{21}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Reduce the fraction \frac{9}{21} to lowest terms by extracting and canceling out 3.

$$\sqrt{0+\frac{9}{4}\times \frac{3}{7}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Multiply \frac{9}{4} and \frac{3}{7} to get \frac{27}{28}.

$$\sqrt{0+\frac{27}{28}\left(\frac{11}{15}+\frac{1}{5}\right)\times \frac{5}{3}\times \frac{3}{2}}$$

Add \frac{11}{15} and \frac{1}{5} to get \frac{14}{15}.

$$\sqrt{0+\frac{27}{28}\times \frac{14}{15}\times \frac{5}{3}\times \frac{3}{2}}$$

Multiply \frac{27}{28} and \frac{14}{15} to get \frac{9}{10}.

$$\sqrt{0+\frac{9}{10}\times \frac{5}{3}\times \frac{3}{2}}$$

Multiply \frac{9}{10} and \frac{5}{3} to get \frac{3}{2}.

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

Multiply \frac{3}{2} and \frac{3}{2} to get \frac{9}{4}.

$$\sqrt{0+\frac{9}{4}}$$

Add 0 and \frac{9}{4} to get \frac{9}{4}.

$$\sqrt{\frac{9}{4}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$