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

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

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{6}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{6}$$