Solve sqrt{9/7*[5/6+5/2*1/8-(1-frac{1}{4})^2]+(frac{5}{4}*frac{2}{3}+3^0)*frac{3}{22}+(1-frac{2}{9})}

$$\sqrt { \frac { 9 } { 7 } \times [ \frac { 5 } { 6 } + \frac { 5 } { 2 } \times \frac { 1 } { 8 } - ( 1 - \frac { 1 } { 4 } ) ^ { 2 } ] + ( \frac { 5 } { 4 } \times \frac { 2 } { 3 } + 3 ^ { 0 } ) \times \frac { 3 } { 22 } + ( 1 - \frac { 2 } { 9 } ) }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Multiply \frac{5}{2} and \frac{1}{8} to get \frac{5}{16}.

$$\sqrt{\frac{9}{7}\left(\frac{5}{6}+\frac{5}{16}-\left(1-\frac{1}{4}\right)^{2}\right)+\left(\frac{5}{4}\times \frac{2}{3}+3^{0}\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

Add \frac{5}{6} and \frac{5}{16} to get \frac{55}{48}.

$$\sqrt{\frac{9}{7}\left(\frac{55}{48}-\left(1-\frac{1}{4}\right)^{2}\right)+\left(\frac{5}{4}\times \frac{2}{3}+3^{0}\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

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

$$\sqrt{\frac{9}{7}\left(\frac{55}{48}-\left(\frac{3}{4}\right)^{2}\right)+\left(\frac{5}{4}\times \frac{2}{3}+3^{0}\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\sqrt{\frac{9}{7}\left(\frac{55}{48}-\frac{9}{16}\right)+\left(\frac{5}{4}\times \frac{2}{3}+3^{0}\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

Subtract \frac{9}{16} from \frac{55}{48} to get \frac{7}{12}.

$$\sqrt{\frac{9}{7}\times \frac{7}{12}+\left(\frac{5}{4}\times \frac{2}{3}+3^{0}\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

Multiply \frac{9}{7} and \frac{7}{12} to get \frac{3}{4}.

$$\sqrt{\frac{3}{4}+\left(\frac{5}{4}\times \frac{2}{3}+3^{0}\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

Multiply \frac{5}{4} and \frac{2}{3} to get \frac{5}{6}.

$$\sqrt{\frac{3}{4}+\left(\frac{5}{6}+3^{0}\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

Calculate 3 to the power of 0 and get 1.

$$\sqrt{\frac{3}{4}+\left(\frac{5}{6}+1\right)\times \frac{3}{22}+1-\frac{2}{9}}$$

Add \frac{5}{6} and 1 to get \frac{11}{6}.

$$\sqrt{\frac{3}{4}+\frac{11}{6}\times \frac{3}{22}+1-\frac{2}{9}}$$

Multiply \frac{11}{6} and \frac{3}{22} to get \frac{1}{4}.

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

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

$$\sqrt{1+1-\frac{2}{9}}$$

Add 1 and 1 to get 2.

$$\sqrt{2-\frac{2}{9}}$$

Subtract \frac{2}{9} from 2 to get \frac{16}{9}.

$$\sqrt{\frac{16}{9}}$$

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$