Solve frac{2sqrt{6}}{3sqrt{8}}

$$\frac { 2 \sqrt { 6 } } { 3 \sqrt { 8 } }$$

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Multiply 3 and 2 to get 6.

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

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

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}.

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

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

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

Multiply 3 and 2 to get 6.

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

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

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