Solve sqrt{1/2}*2sqrt{3}=

$$\sqrt { \frac { 1 } { 2 } } \cdot 2 \sqrt { 3 } =$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

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

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

$$\sqrt{6}$$