Evaluate
\frac{4\sqrt{5}}{5}\approx 1.788854382
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\sqrt{5}-\frac{1}{\sqrt{3+2}}
Add 3 and 2 to get 5.
\sqrt{5}-\frac{1}{\sqrt{5}}
Add 3 and 2 to get 5.
\sqrt{5}-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\sqrt{5}-\frac{\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{4}{5}\sqrt{5}
Combine \sqrt{5} and -\frac{\sqrt{5}}{5} to get \frac{4}{5}\sqrt{5}.
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