Solve 5sqrt{8}+sqrt{98}-2sqrt{18}

$$5 \sqrt { 8 } + \sqrt { 98 } - 2 \sqrt { 18 }$$

Evaluate

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

Solution Steps

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}.

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

Multiply 5 and 2 to get 10.

$$10\sqrt{2}+\sqrt{98}-2\sqrt{18}$$

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}.

$$10\sqrt{2}+7\sqrt{2}-2\sqrt{18}$$

Combine 10\sqrt{2} and 7\sqrt{2} to get 17\sqrt{2}.

$$17\sqrt{2}-2\sqrt{18}$$

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}.

$$17\sqrt{2}-2\times 3\sqrt{2}$$

Multiply -2 and 3 to get -6.

$$17\sqrt{2}-6\sqrt{2}$$

Combine 17\sqrt{2} and -6\sqrt{2} to get 11\sqrt{2}.

$$11\sqrt{2}$$