Solve sqrt{{8/3-1/2-[(1+1/3)^2:4/3+frac{1}{5}]*frac{5}{46}+(2-frac{1}{4})}:frac{3}{5}}

$$\sqrt { \{ \frac { 8 } { 3 } - \frac { 1 } { 2 } - [ ( 1 + \frac { 1 } { 3 } ) ^ { 2 } : \frac { 4 } { 3 } + \frac { 1 } { 5 } ] \times \frac { 5 } { 46 } + ( 2 - \frac { 1 } { 4 } ) \} : \frac { 3 } { 5 } }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Subtract \frac{1}{2} from \frac{8}{3} to get \frac{13}{6}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(1+\frac{1}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

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

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(\frac{4}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

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

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\frac{16}{9}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Divide \frac{16}{9} by \frac{4}{3} by multiplying \frac{16}{9} by the reciprocal of \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{16}{9}\times \frac{3}{4}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Multiply \frac{16}{9} and \frac{3}{4} to get \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{4}{3}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Add \frac{4}{3} and \frac{1}{5} to get \frac{23}{15}.

$$\sqrt{\frac{\frac{13}{6}-\frac{23}{15}\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Multiply \frac{23}{15} and \frac{5}{46} to get \frac{1}{6}.

$$\sqrt{\frac{\frac{13}{6}-\frac{1}{6}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Subtract \frac{1}{6} from \frac{13}{6} to get 2.

$$\sqrt{\frac{2+2-\frac{1}{4}}{\frac{3}{5}}}$$

Add 2 and 2 to get 4.

$$\sqrt{\frac{4-\frac{1}{4}}{\frac{3}{5}}}$$

Subtract \frac{1}{4} from 4 to get \frac{15}{4}.

$$\sqrt{\frac{\frac{15}{4}}{\frac{3}{5}}}$$

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

$$\sqrt{\frac{15}{4}\times \frac{5}{3}}$$

Multiply \frac{15}{4} and \frac{5}{3} to get \frac{25}{4}.

$$\sqrt{\frac{25}{4}}$$

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

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$