Solve sqrt{50}+sqrt{72}-sqrt{18}

$$\sqrt { 50 } + \sqrt { 72 } - \sqrt { 18 }$$

Evaluate

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

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}.

$$5\sqrt{2}+\sqrt{72}-\sqrt{18}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$5\sqrt{2}+6\sqrt{2}-\sqrt{18}$$

Combine 5\sqrt{2} and 6\sqrt{2} to get 11\sqrt{2}.

$$11\sqrt{2}-\sqrt{18}$$

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}.

$$11\sqrt{2}-3\sqrt{2}$$

Combine 11\sqrt{2} and -3\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}$$