Solve frac{3sqrt{6}}{6sqrt{3}}=

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

Evaluate

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

Solution Steps

Cancel out 3 in both numerator and denominator.

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

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}.

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