Solve 11501-13^2871286/sqrt{14}

$$11501- { 13 }^{ 2 } \frac{ 871286 }{ \sqrt{ 14 } }$$

Evaluate

$$-\frac{73623667\sqrt{14}}{7}+11501\approx -39342004.353133552$$

Solution Steps

Calculate 13 to the power of 2 and get 169.

$$11501-169\times \frac{871286}{\sqrt{14}}$$

Rationalize the denominator of \frac{871286}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$11501-169\times \frac{871286\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$11501-169\times \frac{871286\sqrt{14}}{14}$$

Divide 871286\sqrt{14} by 14 to get \frac{435643}{7}\sqrt{14}.

$$11501-169\times \frac{435643}{7}\sqrt{14}$$

Express 169\times \frac{435643}{7} as a single fraction.

$$11501-\frac{169\times 435643}{7}\sqrt{14}$$

Multiply 169 and 435643 to get 73623667.

$$11501-\frac{73623667}{7}\sqrt{14}$$

Factor

$$\frac{31 {(2597 - 2374957 \sqrt{14})}}{7} = -39342004.35313355$$