Solve sqrt{12}+frac{sqrt{24}}{2}

$$\sqrt { 12 } + \frac { \sqrt { 24 } } { 2 }$$

Evaluate

$$\sqrt{6}+2\sqrt{3}\approx 5.913591358$$

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}.

$$2\sqrt{3}+\frac{\sqrt{24}}{2}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Cancel out 2 and 2.

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

Factor

$$\sqrt{6} + 2 \sqrt{3} = 5.913591358$$