Solve 1/2*sqrt{6}+sqrt{8}*frac{sqrt{3}}{2}

$$\frac { 1 } { 2 } \times \sqrt { 6 } + \sqrt { 8 } \times \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$\frac{3\sqrt{6}}{2}\approx 3.674234614$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{1}{2}\sqrt{6}+2\sqrt{2}\times \frac{\sqrt{3}}{2}$$

Cancel out 2 and 2.

$$\frac{1}{2}\sqrt{6}+\sqrt{3}\sqrt{2}$$

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

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

Combine \frac{1}{2}\sqrt{6} and \sqrt{6} to get \frac{3}{2}\sqrt{6}.

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