Solve (sqrt{45}+sqrt{18})-sqrt{18}-sqrt{125})

$$( \sqrt { 45 } + \sqrt { 18 } ) - \sqrt { 18 } - \sqrt { 125 } )$$

Evaluate

$$-2\sqrt{5}\approx -4.472135955$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$3\sqrt{5}+\sqrt{18}-\sqrt{18}-\sqrt{125}$$

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}.

$$3\sqrt{5}+3\sqrt{2}-\sqrt{18}-\sqrt{125}$$

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}.

$$3\sqrt{5}+3\sqrt{2}-3\sqrt{2}-\sqrt{125}$$

Combine 3\sqrt{2} and -3\sqrt{2} to get 0.

$$3\sqrt{5}-\sqrt{125}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$3\sqrt{5}-5\sqrt{5}$$

Combine 3\sqrt{5} and -5\sqrt{5} to get -2\sqrt{5}.

$$-2\sqrt{5}$$