Solve sqrt{4/3}*6

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

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Solution Steps

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

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

Calculate the square root of 4 and get 2.

$$6\times \frac{2}{\sqrt{3}}$$

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

$$6\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$6\times \frac{2\sqrt{3}}{3}$$

Cancel out 3, the greatest common factor in 6 and 3.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{3}$$