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

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

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

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

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

The square of \sqrt{6} is 6.

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

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}.

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

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

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

Multiply 2 and 6 to get 12.

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

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{3}}{12}$$

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

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