Solve -sqrt{8}+sqrt{20}-sqrt{18}+sqrt{125}

$$- \sqrt { 8 } + \sqrt { 20 } - \sqrt { 18 } + \sqrt { 125 }$$

Evaluate

$$7\sqrt{5}-5\sqrt{2}\approx 8.581408031$$

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}.

$$-2\sqrt{2}+\sqrt{20}-\sqrt{18}+\sqrt{125}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

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}.

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

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}.

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

Combine 2\sqrt{5} and 5\sqrt{5} to get 7\sqrt{5}.

$$-2\sqrt{2}+7\sqrt{5}-3\sqrt{2}$$

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

$$-5\sqrt{2}+7\sqrt{5}$$