Evaluate
9\sqrt{5}\approx 20.124611797
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10\sqrt{5}-\sqrt{125}+\sqrt{80}
Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.
10\sqrt{5}-5\sqrt{5}+\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}.
5\sqrt{5}+\sqrt{80}
Combine 10\sqrt{5} and -5\sqrt{5} to get 5\sqrt{5}.
5\sqrt{5}+4\sqrt{5}
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}.
9\sqrt{5}
Combine 5\sqrt{5} and 4\sqrt{5} to get 9\sqrt{5}.
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