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2\times \frac{4\sqrt{5}}{5\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{4}{5\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
2\times \frac{4\sqrt{5}}{5\times 5}
The square of \sqrt{5} is 5.
2\times \frac{4\sqrt{5}}{25}
Multiply 5 and 5 to get 25.
\frac{2\times 4\sqrt{5}}{25}
Express 2\times \frac{4\sqrt{5}}{25} as a single fraction.
\frac{8\sqrt{5}}{25}
Multiply 2 and 4 to get 8.