Solve 2/3sqrt{27/4}

$$\frac { 2 } { 3 } \sqrt { \frac { 27 } { 4 } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{27}{4}} as the division of square roots \frac{\sqrt{27}}{\sqrt{4}}.

$$\frac{2}{3}\times \frac{\sqrt{27}}{\sqrt{4}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Calculate the square root of 4 and get 2.

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

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

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

Cancel out 2\times 3 in both numerator and denominator.

$$\sqrt{3}$$