Evaluate
\sqrt{255}+16\approx 31.968719423
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\frac{16+\sqrt{255}}{\left(16-\sqrt{255}\right)\left(16+\sqrt{255}\right)}
Rationalize the denominator of \frac{1}{16-\sqrt{255}} by multiplying numerator and denominator by 16+\sqrt{255}.
\frac{16+\sqrt{255}}{16^{2}-\left(\sqrt{255}\right)^{2}}
Consider \left(16-\sqrt{255}\right)\left(16+\sqrt{255}\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{16+\sqrt{255}}{256-255}
Square 16. Square \sqrt{255}.
\frac{16+\sqrt{255}}{1}
Subtract 255 from 256 to get 1.
16+\sqrt{255}
Anything divided by one gives itself.
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