Solve 11501-13^871286/sqrt{14}

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

Evaluate

$$-\frac{5663359\sqrt{14}}{7}+11501\approx -3015691.719471812$$

Solution Steps

Calculate 13 to the power of 1 and get 13.

$$11501-13\times \frac{871286}{\sqrt{14}}$$

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

$$11501-13\times \frac{871286\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$11501-13\times \frac{871286\sqrt{14}}{14}$$

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

$$11501-13\times \frac{435643}{7}\sqrt{14}$$

Express 13\times \frac{435643}{7} as a single fraction.

$$11501-\frac{13\times 435643}{7}\sqrt{14}$$

Multiply 13 and 435643 to get 5663359.

$$11501-\frac{5663359}{7}\sqrt{14}$$

Factor

$$\frac{31 {(2597 - 182689 \sqrt{14})}}{7} = -3015691.719471812$$