Solve 20-8/frac{10{sqrt{13}}}

$$\frac{ 20-8 }{ \frac{ 10 }{ \sqrt{ 13 } } }$$

Evaluate

$$\frac{6\sqrt{13}}{5}\approx 4.326661531$$

Solution Steps

Subtract 8 from 20 to get 12.

$$\frac{12}{\frac{10}{\sqrt{13}}}$$

Rationalize the denominator of \frac{10}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{12}{\frac{10\sqrt{13}}{\left(\sqrt{13}\right)^{2}}}$$

The square of \sqrt{13} is 13.

$$\frac{12}{\frac{10\sqrt{13}}{13}}$$

Divide 12 by \frac{10\sqrt{13}}{13} by multiplying 12 by the reciprocal of \frac{10\sqrt{13}}{13}.

$$\frac{12\times 13}{10\sqrt{13}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{6\times 13}{5\sqrt{13}}$$

Rationalize the denominator of \frac{6\times 13}{5\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{6\times 13\sqrt{13}}{5\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{6\times 13\sqrt{13}}{5\times 13}$$

Multiply 6 and 13 to get 78.

$$\frac{78\sqrt{13}}{5\times 13}$$

Multiply 5 and 13 to get 65.

$$\frac{78\sqrt{13}}{65}$$

Divide 78\sqrt{13} by 65 to get \frac{6}{5}\sqrt{13}.

$$\frac{6}{5}\sqrt{13}$$