Solve sqrt{2}*sqrt{3}div1/sqrt{2}=

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

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

Divide \sqrt{6} by \frac{\sqrt{2}}{2} by multiplying \sqrt{6} by the reciprocal of \frac{\sqrt{2}}{2}.

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

Rationalize the denominator of \frac{\sqrt{6}\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Cancel out 2 and 2.

$$2\sqrt{3}$$