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

$$\sqrt { \{ ( 1 + \frac { 3 } { 4 } - \frac { 1 } { 2 } ) ^ { 2 } : [ 1 - ( \frac { 5 } { 4 } - \frac { 1 } { 2 } ) ] ^ { 2 } \cdot ( \frac { 2 } { 5 } : \frac { 5 } { 4 } ) \cdot \frac { 1 } { 14 } \} \cdot \frac { 4 } { 7 } }$$

Evaluate

$$\frac{4}{7}\approx 0.571428571$$

Solution Steps

Add 1 and \frac{3}{4} to get \frac{7}{4}.

$$\sqrt{\frac{\left(\frac{7}{4}-\frac{1}{2}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Subtract \frac{1}{2} from \frac{7}{4} to get \frac{5}{4}.

$$\sqrt{\frac{\left(\frac{5}{4}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\sqrt{\frac{\frac{25}{16}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Subtract \frac{1}{2} from \frac{5}{4} to get \frac{3}{4}.

$$\sqrt{\frac{\frac{25}{16}}{\left(1-\frac{3}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Subtract \frac{3}{4} from 1 to get \frac{1}{4}.

$$\sqrt{\frac{\frac{25}{16}}{\left(\frac{1}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\sqrt{\frac{\frac{25}{16}}{\frac{1}{16}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Divide \frac{25}{16} by \frac{1}{16} by multiplying \frac{25}{16} by the reciprocal of \frac{1}{16}.

$$\sqrt{\frac{25}{16}\times 16\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Multiply \frac{25}{16} and 16 to get 25.

$$\sqrt{25\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\times \frac{4}{7}}$$

Divide \frac{2}{5} by \frac{5}{4} by multiplying \frac{2}{5} by the reciprocal of \frac{5}{4}.

$$\sqrt{25\times \frac{2}{5}\times \frac{4}{5}\times \frac{1}{14}\times \frac{4}{7}}$$

Multiply \frac{2}{5} and \frac{4}{5} to get \frac{8}{25}.

$$\sqrt{25\times \frac{8}{25}\times \frac{1}{14}\times \frac{4}{7}}$$

Multiply 25 and \frac{8}{25} to get 8.

$$\sqrt{8\times \frac{1}{14}\times \frac{4}{7}}$$

Multiply 8 and \frac{1}{14} to get \frac{4}{7}.

$$\sqrt{\frac{4}{7}\times \frac{4}{7}}$$

Multiply \frac{4}{7} and \frac{4}{7} to get \frac{16}{49}.

$$\sqrt{\frac{16}{49}}$$

Rewrite the square root of the division \frac{16}{49} as the division of square roots \frac{\sqrt{16}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$\frac{4}{7}$$

Factor

$$\frac{2 ^ {2}}{7} = 0.5714285714285714$$