Evaluate
\frac{2\left(\sqrt{2}+5\right)}{23}\approx 0.557757701
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\frac{2\left(5+\sqrt{2}\right)}{\left(5-\sqrt{2}\right)\left(5+\sqrt{2}\right)}
Rationalize the denominator of \frac{2}{5-\sqrt{2}} by multiplying numerator and denominator by 5+\sqrt{2}.
\frac{2\left(5+\sqrt{2}\right)}{5^{2}-\left(\sqrt{2}\right)^{2}}
Consider \left(5-\sqrt{2}\right)\left(5+\sqrt{2}\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{2\left(5+\sqrt{2}\right)}{25-2}
Square 5. Square \sqrt{2}.
\frac{2\left(5+\sqrt{2}\right)}{23}
Subtract 2 from 25 to get 23.
\frac{10+2\sqrt{2}}{23}
Use the distributive property to multiply 2 by 5+\sqrt{2}.
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