Solve 2sqrt{50}-3sqrt{8}+sqrt{98}

$$2 \sqrt { 50 } - 3 \sqrt { 8 } + \sqrt { 98 }$$

Evaluate

$$11\sqrt{2}\approx 15.556349186$$

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}.

$$2\times 5\sqrt{2}-3\sqrt{8}+\sqrt{98}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{2}-3\sqrt{8}+\sqrt{98}$$

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}.

$$10\sqrt{2}-3\times 2\sqrt{2}+\sqrt{98}$$

Multiply -3 and 2 to get -6.

$$10\sqrt{2}-6\sqrt{2}+\sqrt{98}$$

Combine 10\sqrt{2} and -6\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}+\sqrt{98}$$

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}.

$$4\sqrt{2}+7\sqrt{2}$$

Combine 4\sqrt{2} and 7\sqrt{2} to get 11\sqrt{2}.

$$11\sqrt{2}$$