Solve frac{sqrt{6}}{sqrt{12}}

$$\frac{ \sqrt{ 6 } }{ \sqrt{ 12 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

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

The square of \sqrt{3} is 3.

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

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}.

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

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

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

Multiply 2 and 3 to get 6.

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

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

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