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

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

Evaluate

$$\frac{2\sqrt{3}}{3}\approx 1.154700538$$

Solution Steps

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

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

The square of \sqrt{6} is 6.

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

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 2 to get 4.

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

Divide 4\sqrt{3} by 6 to get \frac{2}{3}\sqrt{3}.

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