Evaluate
10\sqrt{5}\approx 22.360679775
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4\sqrt{5}+\frac{30}{\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}.
4\sqrt{5}+\frac{30\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{30}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
4\sqrt{5}+\frac{30\sqrt{5}}{5}
The square of \sqrt{5} is 5.
4\sqrt{5}+6\sqrt{5}
Divide 30\sqrt{5} by 5 to get 6\sqrt{5}.
10\sqrt{5}
Combine 4\sqrt{5} and 6\sqrt{5} to get 10\sqrt{5}.
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