Solve frac{6+sqrt{24}}{2}

$$\frac { 6 + \sqrt { 24 } } { 2 }$$

Evaluate

$$\sqrt{6}+3\approx 5.449489743$$

Solution Steps

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}.

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

Divide each term of 6+2\sqrt{6} by 2 to get 3+\sqrt{6}.

$$3+\sqrt{6}$$