Solve frac{sqrt{18}+sqrt{72}}{sqrt{8}}

$$\frac{ \sqrt{ 18 } + \sqrt{ 72 } }{ \sqrt{ 8 } }$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

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}.

$$\frac{3\sqrt{2}+\sqrt{72}}{\sqrt{8}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Combine 3\sqrt{2} and 6\sqrt{2} to get 9\sqrt{2}.

$$\frac{9\sqrt{2}}{\sqrt{8}}$$

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}.

$$\frac{9\sqrt{2}}{2\sqrt{2}}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$