Solve 3sqrt{18}-11sqrt{2}+2sqrt{50}

$$3 \sqrt { 18 } - 11 \sqrt { 2 } + 2 \sqrt { 50 }$$

Evaluate

$$8\sqrt{2}\approx 11.313708499$$

Solution Steps

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}.

$$3\times 3\sqrt{2}-11\sqrt{2}+2\sqrt{50}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}-11\sqrt{2}+2\sqrt{50}$$

Combine 9\sqrt{2} and -11\sqrt{2} to get -2\sqrt{2}.

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

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}.

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

Multiply 2 and 5 to get 10.

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

Combine -2\sqrt{2} and 10\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}$$