Solve 2/3sqrt{3/4}

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

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

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

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

Calculate the square root of 4 and get 2.

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

Multiply \frac{2}{3} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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