Solve sqrt{(2/3+9/8*4/3)^2:(27/12-frac{1}{2}-frac{2}{3})-frac{1}{3}}

$$\sqrt { ( \frac { 2 } { 3 } + \frac { 9 } { 8 } \cdot \frac { 4 } { 3 } ) ^ { 2 } : ( \frac { 27 } { 12 } - \frac { 1 } { 2 } - \frac { 2 } { 3 } ) - \frac { 1 } { 3 } }$$

Evaluate

$$2$$

Solution Steps

Multiply \frac{9}{8} and \frac{4}{3} to get \frac{3}{2}.

$$\sqrt{\frac{\left(\frac{2}{3}+\frac{3}{2}\right)^{2}}{\frac{27}{12}-\frac{1}{2}-\frac{2}{3}}-\frac{1}{3}}$$

Add \frac{2}{3} and \frac{3}{2} to get \frac{13}{6}.

$$\sqrt{\frac{\left(\frac{13}{6}\right)^{2}}{\frac{27}{12}-\frac{1}{2}-\frac{2}{3}}-\frac{1}{3}}$$

Calculate \frac{13}{6} to the power of 2 and get \frac{169}{36}.

$$\sqrt{\frac{\frac{169}{36}}{\frac{27}{12}-\frac{1}{2}-\frac{2}{3}}-\frac{1}{3}}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{\frac{169}{36}}{\frac{9}{4}-\frac{1}{2}-\frac{2}{3}}-\frac{1}{3}}$$

Subtract \frac{1}{2} from \frac{9}{4} to get \frac{7}{4}.

$$\sqrt{\frac{\frac{169}{36}}{\frac{7}{4}-\frac{2}{3}}-\frac{1}{3}}$$

Subtract \frac{2}{3} from \frac{7}{4} to get \frac{13}{12}.

$$\sqrt{\frac{\frac{169}{36}}{\frac{13}{12}}-\frac{1}{3}}$$

Divide \frac{169}{36} by \frac{13}{12} by multiplying \frac{169}{36} by the reciprocal of \frac{13}{12}.

$$\sqrt{\frac{169}{36}\times \frac{12}{13}-\frac{1}{3}}$$

Multiply \frac{169}{36} and \frac{12}{13} to get \frac{13}{3}.

$$\sqrt{\frac{13}{3}-\frac{1}{3}}$$

Subtract \frac{1}{3} from \frac{13}{3} to get 4.

$$\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$2$$

Factor

$$2$$