Solve 3sqrt{(1/6})

$$3 \sqrt{ ( \frac{ 1 }{ 6 } } )$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{6} is 6.

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

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

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