Solve frac{frac{sqrt{3}}{2}}{4sqrt{3}}

$$\frac { \frac { \sqrt { 3 } } { 2 } } { 4 \sqrt { 3 } }$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Express \frac{\frac{\sqrt{3}}{2}}{4\sqrt{3}} as a single fraction.

$$\frac{\sqrt{3}}{2\times 4\sqrt{3}}$$

Multiply 2 and 4 to get 8.

$$\frac{\sqrt{3}}{8\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{3}}{8\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}\sqrt{3}}{8\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}\sqrt{3}}{8\times 3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3}{8\times 3}$$

Multiply 8 and 3 to get 24.

$$\frac{3}{24}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$