Solve sqrt{50}+sqrt{72}-sqrt{32}

$$\sqrt{ 50 } + \sqrt{ 72 } - \sqrt{ 32 }$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

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}.

$$5\sqrt{2}+\sqrt{72}-\sqrt{32}$$

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}.

$$5\sqrt{2}+6\sqrt{2}-\sqrt{32}$$

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

$$11\sqrt{2}-\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$11\sqrt{2}-4\sqrt{2}$$

Combine 11\sqrt{2} and -4\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}$$