Solve (sqrt{2}+sqrt{8})+(sqrt{2}+sqrt{8})+(sqrt{2}+sqrt{8})

$$( \sqrt{ 2 } + \sqrt{ 8 } )+( \sqrt{ 2 } + \sqrt{ 8 } )+( \sqrt{ 2 } + \sqrt{ 8 } )$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

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}.

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

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

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

Combine 3\sqrt{2} and \sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}+\sqrt{8}+\sqrt{2}+\sqrt{8}$$

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}.

$$4\sqrt{2}+2\sqrt{2}+\sqrt{2}+\sqrt{8}$$

Combine 4\sqrt{2} and 2\sqrt{2} to get 6\sqrt{2}.

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

Combine 6\sqrt{2} and \sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}+\sqrt{8}$$

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}.

$$7\sqrt{2}+2\sqrt{2}$$

Combine 7\sqrt{2} and 2\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}$$