Solve sqrt{50}+sqrt{98}-sqrt{2}+sqrt{8}

$$\sqrt { 50 } + \sqrt { 98 } - \sqrt { 2 } + \sqrt { 8 }$$

Evaluate

$$13\sqrt{2}\approx 18.384776311$$

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}.

$$5\sqrt{2}+\sqrt{98}-\sqrt{2}+\sqrt{8}$$

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}.

$$5\sqrt{2}+7\sqrt{2}-\sqrt{2}+\sqrt{8}$$

Combine 5\sqrt{2} and 7\sqrt{2} to get 12\sqrt{2}.

$$12\sqrt{2}-\sqrt{2}+\sqrt{8}$$

Combine 12\sqrt{2} and -\sqrt{2} to get 11\sqrt{2}.

$$11\sqrt{2}+\sqrt{8}$$

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}.

$$11\sqrt{2}+2\sqrt{2}$$

Combine 11\sqrt{2} and 2\sqrt{2} to get 13\sqrt{2}.

$$13\sqrt{2}$$