Solve 2(3/sqrt{3})(2/sqrt{13})

$$2 ( \frac { 3 } { \sqrt { 3 } } ) ( \frac { 2 } { \sqrt { 13 } } )$$

Evaluate

$$\frac{4\sqrt{39}}{13}\approx 1.921537846$$

Solution Steps

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

$$2\times \frac{3\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times \frac{2}{\sqrt{13}}$$

The square of \sqrt{3} is 3.

$$2\times \frac{3\sqrt{3}}{3}\times \frac{2}{\sqrt{13}}$$

Cancel out 3 and 3.

$$2\sqrt{3}\times \frac{2}{\sqrt{13}}$$

Rationalize the denominator of \frac{2}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$2\sqrt{3}\times \frac{2\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$2\sqrt{3}\times \frac{2\sqrt{13}}{13}$$

Express 2\times \frac{2\sqrt{13}}{13} as a single fraction.

$$\frac{2\times 2\sqrt{13}}{13}\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{13}}{13}\sqrt{3}$$

Express \frac{4\sqrt{13}}{13}\sqrt{3} as a single fraction.

$$\frac{4\sqrt{13}\sqrt{3}}{13}$$

To multiply \sqrt{13} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{4\sqrt{39}}{13}$$