Evaluate
\frac{7\left(\sqrt{5}+8\right)}{59}\approx 1.214448743
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\frac{7\left(8+\sqrt{5}\right)}{\left(8-\sqrt{5}\right)\left(8+\sqrt{5}\right)}
Rationalize the denominator of \frac{7}{8-\sqrt{5}} by multiplying numerator and denominator by 8+\sqrt{5}.
\frac{7\left(8+\sqrt{5}\right)}{8^{2}-\left(\sqrt{5}\right)^{2}}
Consider \left(8-\sqrt{5}\right)\left(8+\sqrt{5}\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{7\left(8+\sqrt{5}\right)}{64-5}
Square 8. Square \sqrt{5}.
\frac{7\left(8+\sqrt{5}\right)}{59}
Subtract 5 from 64 to get 59.
\frac{56+7\sqrt{5}}{59}
Use the distributive property to multiply 7 by 8+\sqrt{5}.
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