Solve sqrt{50}+sqrt{2}-2sqrt{18}+sqrt{8}

$$\sqrt { 50 } + \sqrt { 2 } - 2 \sqrt { 18 } + \sqrt { 8 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$5\sqrt{2}+\sqrt{2}-2\sqrt{18}+\sqrt{8}$$

Combine 5\sqrt{2} and \sqrt{2} to get 6\sqrt{2}.

$$6\sqrt{2}-2\sqrt{18}+\sqrt{8}$$

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}.

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

Multiply -2 and 3 to get -6.

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

Combine 6\sqrt{2} and -6\sqrt{2} to get 0.

$$\sqrt{8}$$

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}.

$$2\sqrt{2}$$