Solve {left({left(5/16-1/6right)}^2-4/3-{left(-1/3right)}^2-frac{23}{27}right)}^2-frac{1}{3}+2+frac{1}{2}=

$${ \left( { \left( \frac{ 5 }{ 16 } - \frac{ 1 }{ 6 } \right) }^{ 2 } - \frac{ 4 }{ 3 } - { \left(- \frac{ 1 }{ 3 } \right) }^{ 2 } - \frac{ 23 }{ 27 } \right) }^{ 2 } - \frac{ 1 }{ 3 } +2+ \frac{ 1 }{ 2 } =$$

Evaluate

$$\frac{350789737}{47775744}\approx 7.342423323$$

Solution Steps

Subtract \frac{1}{6} from \frac{5}{16} to get \frac{7}{48}.

$$\left(\left(\frac{7}{48}\right)^{2}-\frac{4}{3}-\left(-\frac{1}{3}\right)^{2}-\frac{23}{27}\right)^{2}-\frac{1}{3}+2+\frac{1}{2}$$

Calculate \frac{7}{48} to the power of 2 and get \frac{49}{2304}.

$$\left(\frac{49}{2304}-\frac{4}{3}-\left(-\frac{1}{3}\right)^{2}-\frac{23}{27}\right)^{2}-\frac{1}{3}+2+\frac{1}{2}$$

Subtract \frac{4}{3} from \frac{49}{2304} to get -\frac{3023}{2304}.

$$\left(-\frac{3023}{2304}-\left(-\frac{1}{3}\right)^{2}-\frac{23}{27}\right)^{2}-\frac{1}{3}+2+\frac{1}{2}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\left(-\frac{3023}{2304}-\frac{1}{9}-\frac{23}{27}\right)^{2}-\frac{1}{3}+2+\frac{1}{2}$$

Subtract \frac{1}{9} from -\frac{3023}{2304} to get -\frac{1093}{768}.

$$\left(-\frac{1093}{768}-\frac{23}{27}\right)^{2}-\frac{1}{3}+2+\frac{1}{2}$$

Subtract \frac{23}{27} from -\frac{1093}{768} to get -\frac{15725}{6912}.

$$\left(-\frac{15725}{6912}\right)^{2}-\frac{1}{3}+2+\frac{1}{2}$$

Calculate -\frac{15725}{6912} to the power of 2 and get \frac{247275625}{47775744}.

$$\frac{247275625}{47775744}-\frac{1}{3}+2+\frac{1}{2}$$

Subtract \frac{1}{3} from \frac{247275625}{47775744} to get \frac{231350377}{47775744}.

$$\frac{231350377}{47775744}+2+\frac{1}{2}$$

Add \frac{231350377}{47775744} and 2 to get \frac{326901865}{47775744}.

$$\frac{326901865}{47775744}+\frac{1}{2}$$

Add \frac{326901865}{47775744} and \frac{1}{2} to get \frac{350789737}{47775744}.

$$\frac{350789737}{47775744}$$

Factor

$$\frac{350789737}{2 ^ {16} \cdot 3 ^ {6}} = 7\frac{16359529}{47775744} = 7.342423322596504$$