Solve sqrt{72}-sqrt{800}-sqrt{18}

$$\sqrt { 72 } - \sqrt { 800 } - \sqrt { 18 }$$

Evaluate

$$-17\sqrt{2}\approx -24.04163056$$

Solution Steps

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}.

$$6\sqrt{2}-\sqrt{800}-\sqrt{18}$$

Factor 800=20^{2}\times 2. Rewrite the square root of the product \sqrt{20^{2}\times 2} as the product of square roots \sqrt{20^{2}}\sqrt{2}. Take the square root of 20^{2}.

$$6\sqrt{2}-20\sqrt{2}-\sqrt{18}$$

Combine 6\sqrt{2} and -20\sqrt{2} to get -14\sqrt{2}.

$$-14\sqrt{2}-\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$-14\sqrt{2}-3\sqrt{2}$$

Combine -14\sqrt{2} and -3\sqrt{2} to get -17\sqrt{2}.

$$-17\sqrt{2}$$