Solve sqrt{50}-sqrt{72}-2sqrt{2}=

$$\sqrt { 50 } - \sqrt { 72 } - 2 \sqrt { 2 } =$$

Evaluate

$$-3\sqrt{2}\approx -4.242640687$$

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}.

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

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}.

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

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

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

Combine -\sqrt{2} and -2\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}$$