Solve 3+sqrt{6}+sqrt{6}+2+3-sqrt{6}-sqrt{8}+2

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

Evaluate

$$\sqrt{6}+10-2\sqrt{2}\approx 9.621062618$$

Solution Steps

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

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

Add 3 and 2 to get 5.

$$5+2\sqrt{6}+3-\sqrt{6}-\sqrt{8}+2$$

Add 5 and 3 to get 8.

$$8+2\sqrt{6}-\sqrt{6}-\sqrt{8}+2$$

Combine 2\sqrt{6} and -\sqrt{6} to get \sqrt{6}.

$$8+\sqrt{6}-\sqrt{8}+2$$

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}.

$$8+\sqrt{6}-2\sqrt{2}+2$$

Add 8 and 2 to get 10.

$$10+\sqrt{6}-2\sqrt{2}$$