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

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

Evaluate

$$\frac{\sqrt{6}}{12}\approx 0.204124145$$

Solution Steps

Calculate the square root of 4 and get 2.

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

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

$$\frac{\sqrt{2}}{4}\times \frac{2\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{\sqrt{2}}{4} times \frac{\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{\sqrt{6}}{4\times 3}$$

Multiply 4 and 3 to get 12.

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