Solve frac{sqrt{216}+sqrt{54}+sqrt{150}}{sqrt{96}}

$$\frac{ \sqrt{ 216 } + \sqrt{ 54 } + \sqrt{ 150 } }{ \sqrt{ 96 } }$$

Evaluate

$$\frac{7}{2}=3.5$$

Solution Steps

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$\frac{6\sqrt{6}+\sqrt{54}+\sqrt{150}}{\sqrt{96}}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{6\sqrt{6}+3\sqrt{6}+\sqrt{150}}{\sqrt{96}}$$

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

$$\frac{9\sqrt{6}+\sqrt{150}}{\sqrt{96}}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$\frac{9\sqrt{6}+5\sqrt{6}}{\sqrt{96}}$$

Combine 9\sqrt{6} and 5\sqrt{6} to get 14\sqrt{6}.

$$\frac{14\sqrt{6}}{\sqrt{96}}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$\frac{14\sqrt{6}}{4\sqrt{6}}$$

Cancel out 2\sqrt{6} in both numerator and denominator.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$