Solve 4sqrt{3}*2/sqrt{3}

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

Evaluate

$$8$$

Solution Steps

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

$$4\sqrt{3}\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Express 4\times \frac{2\sqrt{3}}{3} as a single fraction.

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

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{3}}{3}\sqrt{3}$$

Express \frac{8\sqrt{3}}{3}\sqrt{3} as a single fraction.

$$\frac{8\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{8\times 3}{3}$$

Cancel out 3 and 3.

$$8$$

Factor

$$2^{3}$$