Solve sqrt{5}+sqrt{20}-sqrt{80}-sqrt{125}

$$\sqrt { 5 } + \sqrt { 20 } - \sqrt { 80 } - \sqrt { 125 }$$

Evaluate

$$-6\sqrt{5}\approx -13.416407865$$

Solution Steps

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}.

$$\sqrt{5}+2\sqrt{5}-\sqrt{80}-\sqrt{125}$$

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

$$3\sqrt{5}-\sqrt{80}-\sqrt{125}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$3\sqrt{5}-4\sqrt{5}-\sqrt{125}$$

Combine 3\sqrt{5} and -4\sqrt{5} to get -\sqrt{5}.

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

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}.

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

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

$$-6\sqrt{5}$$