Solve sqrt{16/12}

$$\sqrt{ \frac{ 16 }{ 12 } }$$

Evaluate

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

Solution Steps

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

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

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

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

Calculate the square root of 4 and get 2.

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

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

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

The square of \sqrt{3} is 3.

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