Solve sqrt{17/12+9/7:{2/5+7/8:[(frac{11}{15}-frac{1}{3})^2:(frac{8}{5})^2+(frac{5}{2}-frac{9}{8}-frac{9}{16})]^2}}

$$\sqrt { \frac { 17 } { 12 } + \frac { 9 } { 7 } : \{ \frac { 2 } { 5 } + \frac { 7 } { 8 } : [ ( \frac { 11 } { 15 } - \frac { 1 } { 3 } ) ^ { 2 } : ( \frac { 8 } { 5 } ) ^ { 2 } + ( \frac { 5 } { 2 } - \frac { 9 } { 8 } - \frac { 9 } { 16 } ) ] ^ { 2 } \} }$$

Evaluate

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

Solution Steps

Subtract \frac{1}{3} from \frac{11}{15} to get \frac{2}{5}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{\left(\frac{2}{5}\right)^{2}}{\left(\frac{8}{5}\right)^{2}}+\frac{5}{2}-\frac{9}{8}-\frac{9}{16}\right)^{2}}}}$$

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

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{\frac{4}{25}}{\left(\frac{8}{5}\right)^{2}}+\frac{5}{2}-\frac{9}{8}-\frac{9}{16}\right)^{2}}}}$$

Calculate \frac{8}{5} to the power of 2 and get \frac{64}{25}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{\frac{4}{25}}{\frac{64}{25}}+\frac{5}{2}-\frac{9}{8}-\frac{9}{16}\right)^{2}}}}$$

Divide \frac{4}{25} by \frac{64}{25} by multiplying \frac{4}{25} by the reciprocal of \frac{64}{25}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{4}{25}\times \frac{25}{64}+\frac{5}{2}-\frac{9}{8}-\frac{9}{16}\right)^{2}}}}$$

Multiply \frac{4}{25} and \frac{25}{64} to get \frac{1}{16}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{1}{16}+\frac{5}{2}-\frac{9}{8}-\frac{9}{16}\right)^{2}}}}$$

Add \frac{1}{16} and \frac{5}{2} to get \frac{41}{16}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{41}{16}-\frac{9}{8}-\frac{9}{16}\right)^{2}}}}$$

Subtract \frac{9}{8} from \frac{41}{16} to get \frac{23}{16}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{23}{16}-\frac{9}{16}\right)^{2}}}}$$

Subtract \frac{9}{16} from \frac{23}{16} to get \frac{7}{8}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\left(\frac{7}{8}\right)^{2}}}}$$

Calculate \frac{7}{8} to the power of 2 and get \frac{49}{64}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{\frac{7}{8}}{\frac{49}{64}}}}$$

Divide \frac{7}{8} by \frac{49}{64} by multiplying \frac{7}{8} by the reciprocal of \frac{49}{64}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{7}{8}\times \frac{64}{49}}}$$

Multiply \frac{7}{8} and \frac{64}{49} to get \frac{8}{7}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{2}{5}+\frac{8}{7}}}$$

Add \frac{2}{5} and \frac{8}{7} to get \frac{54}{35}.

$$\sqrt{\frac{17}{12}+\frac{\frac{9}{7}}{\frac{54}{35}}}$$

Divide \frac{9}{7} by \frac{54}{35} by multiplying \frac{9}{7} by the reciprocal of \frac{54}{35}.

$$\sqrt{\frac{17}{12}+\frac{9}{7}\times \frac{35}{54}}$$

Multiply \frac{9}{7} and \frac{35}{54} to get \frac{5}{6}.

$$\sqrt{\frac{17}{12}+\frac{5}{6}}$$

Add \frac{17}{12} and \frac{5}{6} 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

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