Solve frac{sqrt{8}}{4sqrt{6}}

$$\frac{ \sqrt{ 8 } }{ 4 \sqrt{ 6 } }$$

Evaluate

$$\frac{\sqrt{3}}{6}\approx 0.288675135$$

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}.

$$\frac{2\sqrt{2}}{4\sqrt{6}}$$

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{6} is 6.

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

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}.

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

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

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

Multiply 2 and 6 to get 12.

$$\frac{2\sqrt{3}}{12}$$

Divide 2\sqrt{3} by 12 to get \frac{1}{6}\sqrt{3}.

$$\frac{1}{6}\sqrt{3}$$