Solve 24/7/sqrt{3}+24/7

$$\frac{ \frac{ 24 }{ 7 } }{ \sqrt{ 3 } } + \frac{ 24 }{ 7 }$$

Evaluate

$$\frac{8\sqrt{3}+24}{7}\approx 5.408058066$$

Short Solution Steps

Express \frac{\frac{24}{7}}{\sqrt{3}} as a single fraction.

$$\frac{24}{7\sqrt{3}}+\frac{24}{7}$$

Rationalize the denominator of \frac{24}{7\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{24\sqrt{3}}{7\left(\sqrt{3}\right)^{2}}+\frac{24}{7}$$

The square of \sqrt{3} is 3.

$$\frac{24\sqrt{3}}{7\times 3}+\frac{24}{7}$$

Cancel out 3 in both numerator and denominator.

$$\frac{8\sqrt{3}}{7}+\frac{24}{7}$$

Since \frac{8\sqrt{3}}{7} and \frac{24}{7} have the same denominator, add them by adding their numerators.

$$\frac{8\sqrt{3}+24}{7}$$

Factor

$$\frac{8 \sqrt{3} {(\sqrt{3} + 1)}}{7} = 5.408058065793002$$