Solve sqrt{50}-sqrt{18}+sqrt{98}

$$\sqrt { 50 } - \sqrt { 18 } + \sqrt { 98 }$$

Evaluate

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

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}.

$$5\sqrt{2}-\sqrt{18}+\sqrt{98}$$

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}.

$$5\sqrt{2}-3\sqrt{2}+\sqrt{98}$$

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

$$2\sqrt{2}+\sqrt{98}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

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

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

$$9\sqrt{2}$$