Solve 4/1*2/sqrt{3}*frac{sqrt{2}}{2}

$$\frac { 4 } { 1 } \cdot \frac { 2 } { \sqrt { 3 } } \cdot \frac { \sqrt { 2 } } { 2 }$$

Evaluate

$$\frac{4\sqrt{6}}{3}\approx 3.265986324$$

Solution Steps

Anything divided by one gives itself.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

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

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

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