Solve sqrt{32}-sqrt{50}

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

Evaluate

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

Solution Steps

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}.

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

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}.

$$4\sqrt{2}-5\sqrt{2}$$

Combine 4\sqrt{2} and -5\sqrt{2} to get -\sqrt{2}.

$$-\sqrt{2}$$