\sqrt { \sqrt { 5 } ( \sqrt { 5 } - \frac { 2 } { \sqrt { 5 } } } )
Evaluate
\sqrt{3}\approx 1.732050808
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\sqrt{\sqrt{5}\left(\sqrt{5}-\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)}
Rationalize the denominator of \frac{2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\sqrt{\sqrt{5}\left(\sqrt{5}-\frac{2\sqrt{5}}{5}\right)}
The square of \sqrt{5} is 5.
\sqrt{\sqrt{5}\times \frac{3}{5}\sqrt{5}}
Combine \sqrt{5} and -\frac{2\sqrt{5}}{5} to get \frac{3}{5}\sqrt{5}.
\sqrt{5\times \frac{3}{5}}
Multiply \sqrt{5} and \sqrt{5} to get 5.
\sqrt{3}
Cancel out 5 and 5.
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