Evaluate
31\sqrt{5}\approx 69.318107302
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\sqrt{5}+2\sqrt{5}+\sqrt{125}+\sqrt{2645}
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}.
3\sqrt{5}+\sqrt{125}+\sqrt{2645}
Combine \sqrt{5} and 2\sqrt{5} to get 3\sqrt{5}.
3\sqrt{5}+5\sqrt{5}+\sqrt{2645}
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}.
8\sqrt{5}+\sqrt{2645}
Combine 3\sqrt{5} and 5\sqrt{5} to get 8\sqrt{5}.
8\sqrt{5}+23\sqrt{5}
Factor 2645=23^{2}\times 5. Rewrite the square root of the product \sqrt{23^{2}\times 5} as the product of square roots \sqrt{23^{2}}\sqrt{5}. Take the square root of 23^{2}.
31\sqrt{5}
Combine 8\sqrt{5} and 23\sqrt{5} to get 31\sqrt{5}.
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