Solve sqrt{2}-sqrt{8}-sqrt{50}

$$\sqrt { 2 } - \sqrt { 8 } - \sqrt { 50 }$$

Evaluate

$$-6\sqrt{2}\approx -8.485281374$$

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}.

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

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

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

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}.

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

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

$$-6\sqrt{2}$$