Solve sqrt{3/18}*sqrt{6}

$$\sqrt { \frac { 3 } { 18 } } \cdot \sqrt { 6 }$$

Evaluate

$$1$$

Solution Steps

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

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

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{6} is 6.

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

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

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6}{6}$$

Divide 6 by 6 to get 1.

$$1$$

Factor

$$1$$