Solve sqrt{50}+sqrt{72}-sqrt{2}?

$$\sqrt { 50 } + \sqrt { 72 } - \sqrt { 2 } ?$$

Evaluate

$$10\sqrt{2}\approx 14.142135624$$

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}.

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

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}.

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

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

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

Combine 11\sqrt{2} and -\sqrt{2} to get 10\sqrt{2}.

$$10\sqrt{2}$$