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

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

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

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}.

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

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}.

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

Combine 5\sqrt{2} and 3\sqrt{2} to get 8\sqrt{2}.

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

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}.

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

Combine 8\sqrt{2} and -2\sqrt{2} to get 6\sqrt{2}.

$$6\sqrt{2}$$