Solve 4sqrt{1/12}

$$4 \sqrt{ \frac{ 1 }{ 12 } }$$

Evaluate

$$\frac{2\sqrt{3}}{3}\approx 1.154700538$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{12}} as the division of square roots \frac{\sqrt{1}}{\sqrt{12}}.

$$4\times \frac{\sqrt{1}}{\sqrt{12}}$$

Calculate the square root of 1 and get 1.

$$4\times \frac{1}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$4\times \frac{1}{2\sqrt{3}}$$

Rationalize the denominator of \frac{1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$4\times \frac{\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\times \frac{\sqrt{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$4\times \frac{\sqrt{3}}{6}$$

Express 4\times \frac{\sqrt{3}}{6} as a single fraction.

$$\frac{4\sqrt{3}}{6}$$

Divide 4\sqrt{3} by 6 to get \frac{2}{3}\sqrt{3}.

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