Solve 3sqrt{(4/3)}

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

Evaluate

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

Solution Steps

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

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

Calculate the square root of 4 and get 2.

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

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

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

The square of \sqrt{3} is 3.

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

Cancel out 3 and 3.

$$2\sqrt{3}$$