Solve 6sqrt{1/3}

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

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

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

$$2\sqrt{3}$$