Solve sqrt{18}*1/sqrt{6}

$$\sqrt { 18 } \times \frac { 1 } { \sqrt { 6 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$3\sqrt{2}\times \frac{1}{\sqrt{6}}$$

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Cancel out 6, the greatest common factor in 3 and 6.

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

Express \frac{\sqrt{6}}{2}\sqrt{2} as a single fraction.

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

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}.

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

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

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

Cancel out 2 and 2.

$$\sqrt{3}$$