Solve sqrt{6}divsqrt{2}*1/sqrt{2}

$$\sqrt { 6 } \div \sqrt { 2 } \times \frac { 1 } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Rewrite the division of square roots \frac{\sqrt{6}}{\sqrt{2}} as the square root of the division \sqrt{\frac{6}{2}} and perform the division.

$$\sqrt{3}\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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

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

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

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