Solve frac{sqrt{left(7-64right)^2}+{left(-12/7-64/17right)}^2}{2}

$$\frac{ \sqrt{ { \left(7-64 \right) }^{ 2 } } + { \left(- \frac{ 12 }{ 7 } - \frac{ 64 }{ 17 } \right) }^{ 2 } }{ 2 }$$

Evaluate

$$\frac{1232281}{28322}\approx 43.509674458$$

Solution Steps

Subtract 64 from 7 to get -57.

$$\frac{\sqrt{\left(-57\right)^{2}}+\left(-\frac{12}{7}-\frac{64}{17}\right)^{2}}{2}$$

Calculate -57 to the power of 2 and get 3249.

$$\frac{\sqrt{3249}+\left(-\frac{12}{7}-\frac{64}{17}\right)^{2}}{2}$$

Calculate the square root of 3249 and get 57.

$$\frac{57+\left(-\frac{12}{7}-\frac{64}{17}\right)^{2}}{2}$$

Subtract \frac{64}{17} from -\frac{12}{7} to get -\frac{652}{119}.

$$\frac{57+\left(-\frac{652}{119}\right)^{2}}{2}$$

Calculate -\frac{652}{119} to the power of 2 and get \frac{425104}{14161}.

$$\frac{57+\frac{425104}{14161}}{2}$$

Add 57 and \frac{425104}{14161} to get \frac{1232281}{14161}.

$$\frac{\frac{1232281}{14161}}{2}$$

Express \frac{\frac{1232281}{14161}}{2} as a single fraction.

$$\frac{1232281}{14161\times 2}$$

Multiply 14161 and 2 to get 28322.

$$\frac{1232281}{28322}$$

Factor

$$\frac{31 \cdot 127 \cdot 313}{2 \cdot 7 ^ {2} \cdot 17 ^ {2}} = 43\frac{14435}{28322} = 43.5096744580185$$