Evaluate
\sqrt{5}-1\approx 1.236067977
Factor
\sqrt{5} - 1 = 1.236067977
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\frac{\left(5-\sqrt{5}\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{5-\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{\left(5-\sqrt{5}\right)\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{5\sqrt{5}-\left(\sqrt{5}\right)^{2}}{5}
Use the distributive property to multiply 5-\sqrt{5} by \sqrt{5}.
\frac{5\sqrt{5}-5}{5}
The square of \sqrt{5} is 5.
\sqrt{5}-1
Divide each term of 5\sqrt{5}-5 by 5 to get \sqrt{5}-1.
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Limits
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