Solve sqrt{18}-sqrt{72}

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

Evaluate

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

Solution Steps

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}.

$$3\sqrt{2}-\sqrt{72}$$

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}.

$$3\sqrt{2}-6\sqrt{2}$$

Combine 3\sqrt{2} and -6\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}$$