Solve sqrt{18}-sqrt{54}+2sqrt{50}

$$\sqrt { 18 } - \sqrt { 54 } + 2 \sqrt { 50 }$$

Evaluate

$$13\sqrt{2}-3\sqrt{6}\approx 11.036307083$$

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}.

$$3\sqrt{2}-\sqrt{54}+2\sqrt{50}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\sqrt{2}-3\sqrt{6}+2\sqrt{50}$$

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}.

$$3\sqrt{2}-3\sqrt{6}+2\times 5\sqrt{2}$$

Multiply 2 and 5 to get 10.

$$3\sqrt{2}-3\sqrt{6}+10\sqrt{2}$$

Combine 3\sqrt{2} and 10\sqrt{2} to get 13\sqrt{2}.

$$13\sqrt{2}-3\sqrt{6}$$