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

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

Evaluate

$$8\sqrt{5}\approx 17.88854382$$

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}.

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

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}.

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

Combine 2\sqrt{5} and -4\sqrt{5} to get -2\sqrt{5}.

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

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}.

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

Multiply 2 and 5 to get 10.

$$-2\sqrt{5}+10\sqrt{5}$$

Combine -2\sqrt{5} and 10\sqrt{5} to get 8\sqrt{5}.

$$8\sqrt{5}$$