Evaluate
\frac{\sqrt{21}+6}{15}\approx 0.705505046
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\frac{6+\sqrt{21}}{\left(6-\sqrt{21}\right)\left(6+\sqrt{21}\right)}
Rationalize the denominator of \frac{1}{6-\sqrt{21}} by multiplying numerator and denominator by 6+\sqrt{21}.
\frac{6+\sqrt{21}}{6^{2}-\left(\sqrt{21}\right)^{2}}
Consider \left(6-\sqrt{21}\right)\left(6+\sqrt{21}\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{6+\sqrt{21}}{36-21}
Square 6. Square \sqrt{21}.
\frac{6+\sqrt{21}}{15}
Subtract 21 from 36 to get 15.
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