Solve sqrt{72}+sqrt{50}-sqrt{162}

$$\sqrt { 72 } + \sqrt { 50 } - \sqrt { 162 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

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}.

$$6\sqrt{2}+\sqrt{50}-\sqrt{162}$$

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}.

$$6\sqrt{2}+5\sqrt{2}-\sqrt{162}$$

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

$$11\sqrt{2}-\sqrt{162}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

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

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

$$2\sqrt{2}$$