Solve sqrt{3}divsqrt{2}*sqrt{6}

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

Evaluate

$$3$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

Express \frac{\sqrt{6}}{2}\sqrt{6} as a single fraction.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$3$$

Factor

$$3$$