Solve frac{sqrt{2}}{2}*2sqrt{12}

$$\frac { \sqrt { 2 } } { 2 } \times 2 \sqrt { 12 }$$

Evaluate

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

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

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

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

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

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

$$2\sqrt{6}$$