Solve 11.501((8.713-10)/sqrt{14})

$$11.501( \frac{ (8.713-10) }{ \sqrt{ 14 } } )$$

Evaluate

$$-\frac{2114541\sqrt{14}}{2000000}\approx -3.955943976$$

Solution Steps

Subtract 10 from 8.713 to get -1.287.

$$11.501\times \frac{-1.287}{\sqrt{14}}$$

Rationalize the denominator of \frac{-1.287}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$11.501\times \frac{-1.287\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$11.501\times \frac{-1.287\sqrt{14}}{14}$$

Divide -1.287\sqrt{14} by 14 to get -\frac{1287}{14000}\sqrt{14}.

$$11.501\left(-\frac{1287}{14000}\right)\sqrt{14}$$

Multiply 11.501 and -\frac{1287}{14000} to get -1.0572705.

$$-1.0572705\sqrt{14}$$