Solve 6/5sqrt{3}*frac{5sqrt{3}}{5sqrt{3}}

$$\frac{ 6 }{ 5 \sqrt{ 3 } } \times \frac{ 5 \sqrt{ 3 } }{ 5 \sqrt{ 3 } }$$

Evaluate

$$\frac{2\sqrt{3}}{5}\approx 0.692820323$$

Solution Steps

Divide 5\sqrt{3} by 5\sqrt{3} to get 1.

$$\frac{6}{5\sqrt{3}}\times 1$$

Rationalize the denominator of \frac{6}{5\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{6\sqrt{3}}{5\left(\sqrt{3}\right)^{2}}\times 1$$

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{3}}{5\times 3}\times 1$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\sqrt{3}}{5}\times 1$$

Express \frac{2\sqrt{3}}{5}\times 1 as a single fraction.

$$\frac{2\sqrt{3}}{5}$$