Solve sqrt{8}+sqrt{32}-sqrt{50}

$$\sqrt{ 8 } + \sqrt{ 32 } - \sqrt{ 50 }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+\sqrt{32}-\sqrt{50}$$

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}.

$$2\sqrt{2}+4\sqrt{2}-\sqrt{50}$$

Combine 2\sqrt{2} and 4\sqrt{2} to get 6\sqrt{2}.

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

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}.

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

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

$$\sqrt{2}$$