Solve sqrt{2}+sqrt{50}+sqrt{18}+sqrt{98}

$$\sqrt { 2 } + \sqrt { 50 } + \sqrt { 18 } + \sqrt { 98 }$$

Evaluate

$$16\sqrt{2}\approx 22.627416998$$

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}.

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

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

$$6\sqrt{2}+\sqrt{18}+\sqrt{98}$$

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}.

$$6\sqrt{2}+3\sqrt{2}+\sqrt{98}$$

Combine 6\sqrt{2} and 3\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}+\sqrt{98}$$

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}.

$$9\sqrt{2}+7\sqrt{2}$$

Combine 9\sqrt{2} and 7\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}$$