Solve frac{sqrt{8}+sqrt{18}}{2}

$$\frac { \sqrt { 8 } + \sqrt { 18 } } { 2 }$$

Evaluate

$$\frac{5\sqrt{2}}{2}\approx 3.535533906$$

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}.

$$\frac{2\sqrt{2}+\sqrt{18}}{2}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.

$$\frac{5\sqrt{2}}{2}$$