Solve frac{sqrt{3}+sqrt{6}+sqrt{2}+1+2sqrt{8}}{2}

$$\frac{ \sqrt{ 3 } + \sqrt{ 6 } + \sqrt{ 2 } +1+2 \sqrt{ 8 } }{ 2 }$$

Evaluate

$$\frac{\sqrt{3}+\sqrt{6}+5\sqrt{2}+1}{2}\approx 6.126304181$$

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}.

$$\frac{\sqrt{3}+\sqrt{6}+\sqrt{2}+1+2\times 2\sqrt{2}}{2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{3}+\sqrt{6}+\sqrt{2}+1+4\sqrt{2}}{2}$$

Combine \sqrt{2} and 4\sqrt{2} to get 5\sqrt{2}.

$$\frac{\sqrt{3}+\sqrt{6}+5\sqrt{2}+1}{2}$$