Evaluate
\sqrt{6}-\sqrt{5}\approx 0.213421765
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\frac{\sqrt{5}-\sqrt{6}}{\left(\sqrt{5}+\sqrt{6}\right)\left(\sqrt{5}-\sqrt{6}\right)}
Rationalize the denominator of \frac{1}{\sqrt{5}+\sqrt{6}} by multiplying numerator and denominator by \sqrt{5}-\sqrt{6}.
\frac{\sqrt{5}-\sqrt{6}}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{6}\right)^{2}}
Consider \left(\sqrt{5}+\sqrt{6}\right)\left(\sqrt{5}-\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{\sqrt{5}-\sqrt{6}}{5-6}
Square \sqrt{5}. Square \sqrt{6}.
\frac{\sqrt{5}-\sqrt{6}}{-1}
Subtract 6 from 5 to get -1.
-\sqrt{5}-\left(-\sqrt{6}\right)
Anything divided by -1 gives its opposite. To find the opposite of \sqrt{5}-\sqrt{6}, find the opposite of each term.
-\sqrt{5}+\sqrt{6}
The opposite of -\sqrt{6} is \sqrt{6}.
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