Solve sqrt{80}-sqrt{125}+2sqrt{20}=

$$\sqrt { 80 } - \sqrt { 125 } + 2 \sqrt { 20 } =$$

Evaluate

$$3\sqrt{5}\approx 6.708203932$$

Solution Steps

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}.

$$4\sqrt{5}-\sqrt{125}+2\sqrt{20}$$

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}.

$$4\sqrt{5}-5\sqrt{5}+2\sqrt{20}$$

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

$$-\sqrt{5}+2\sqrt{20}$$

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}.

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

Multiply 2 and 2 to get 4.

$$-\sqrt{5}+4\sqrt{5}$$

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

$$3\sqrt{5}$$