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

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

Evaluate

$$\frac{\sqrt{2}}{3}\approx 0.471404521$$

Solution Steps

Rationalize the denominator of \frac{2\sqrt{3}}{3\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

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

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

Multiply 3 and 6 to get 18.

$$\frac{2\times 3\sqrt{2}}{18}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}}{18}$$

Divide 6\sqrt{2} by 18 to get \frac{1}{3}\sqrt{2}.

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