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

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

Evaluate

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

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}.

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

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}.

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

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

$$7\sqrt{5}-\sqrt{80}$$

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}.

$$7\sqrt{5}-4\sqrt{5}$$

Combine 7\sqrt{5} and -4\sqrt{5} to get 3\sqrt{5}.

$$3\sqrt{5}$$