Solve 6*5*8/13sqrt{3/8*4}

$$\frac{ 6 \times 5 \times 8 }{ \frac{ 13 \sqrt{ 3 } }{ 8 } \times 4 }$$

Evaluate

$$\frac{160\sqrt{3}}{13}\approx 21.317548401$$

Solution Steps

Multiply 6 and 5 to get 30.

$$\frac{30\times 8}{4\times \frac{13\sqrt{3}}{8}}$$

Multiply 30 and 8 to get 240.

$$\frac{240}{4\times \frac{13\sqrt{3}}{8}}$$

Cancel out 8, the greatest common factor in 4 and 8.

$$\frac{240}{\frac{13\sqrt{3}}{2}}$$

Divide 240 by \frac{13\sqrt{3}}{2} by multiplying 240 by the reciprocal of \frac{13\sqrt{3}}{2}.

$$\frac{240\times 2}{13\sqrt{3}}$$

Rationalize the denominator of \frac{240\times 2}{13\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{240\times 2\sqrt{3}}{13\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{240\times 2\sqrt{3}}{13\times 3}$$

Multiply 240 and 2 to get 480.

$$\frac{480\sqrt{3}}{13\times 3}$$

Multiply 13 and 3 to get 39.

$$\frac{480\sqrt{3}}{39}$$

Divide 480\sqrt{3} by 39 to get \frac{160}{13}\sqrt{3}.

$$\frac{160}{13}\sqrt{3}$$