Solve {left(47/15-4right)}^2+{left(-3/5+3right)}^2

$${ \left( \frac{ 47 }{ 15 } -4 \right) }^{ 2 } + { \left(- \frac{ 3 }{ 5 } +3 \right) }^{ 2 }$$

Evaluate

$$\frac{293}{45}\approx 6.511111111$$

Solution Steps

Subtract 4 from \frac{47}{15} to get -\frac{13}{15}.

$$\left(-\frac{13}{15}\right)^{2}+\left(-\frac{3}{5}+3\right)^{2}$$

Calculate -\frac{13}{15} to the power of 2 and get \frac{169}{225}.

$$\frac{169}{225}+\left(-\frac{3}{5}+3\right)^{2}$$

Add -\frac{3}{5} and 3 to get \frac{12}{5}.

$$\frac{169}{225}+\left(\frac{12}{5}\right)^{2}$$

Calculate \frac{12}{5} to the power of 2 and get \frac{144}{25}.

$$\frac{169}{225}+\frac{144}{25}$$

Add \frac{169}{225} and \frac{144}{25} to get \frac{293}{45}.

$$\frac{293}{45}$$

Factor

$$\frac{293}{3 ^ {2} \cdot 5} = 6\frac{23}{45} = 6.511111111111111$$