Solve frac{frac{sqrt{2}}{2}}{6sqrt{3}}

$$\frac{ \frac{ \sqrt{ 2 } }{ 2 } }{ 6 \sqrt{ 3 } }$$

Evaluate

$$\frac{\sqrt{6}}{36}\approx 0.068041382$$

Solution Steps

Express \frac{\frac{\sqrt{2}}{2}}{6\sqrt{3}} as a single fraction.

$$\frac{\sqrt{2}}{2\times 6\sqrt{3}}$$

Multiply 2 and 6 to get 12.

$$\frac{\sqrt{2}}{12\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{2}}{12\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{2}\sqrt{3}}{12\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{12\times 3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{12\times 3}$$

Multiply 12 and 3 to get 36.

$$\frac{\sqrt{6}}{36}$$