Solve 2sqrt{50}-sqrt{18}+sqrt{8}+1

$$2 \sqrt { 50 } - \sqrt { 18 } + \sqrt { 8 } + 1$$

Evaluate

$$9\sqrt{2}+1\approx 13.727922061$$

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}.

$$2\times 5\sqrt{2}-\sqrt{18}+\sqrt{8}+1$$

Multiply 2 and 5 to get 10.

$$10\sqrt{2}-\sqrt{18}+\sqrt{8}+1$$

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}.

$$10\sqrt{2}-3\sqrt{2}+\sqrt{8}+1$$

Combine 10\sqrt{2} and -3\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}+\sqrt{8}+1$$

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}.

$$7\sqrt{2}+2\sqrt{2}+1$$

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

$$9\sqrt{2}+1$$