Solve sqrt{6}*1/sqrt{3}

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

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Express \sqrt{6}\times \frac{\sqrt{3}}{3} as a single fraction.

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

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}.

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

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

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

Cancel out 3 and 3.

$$\sqrt{2}$$