Evaluate
\frac{2\left(\sqrt{10}+7\right)}{39}\approx 0.521142444
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\frac{2\left(7+\sqrt{10}\right)}{\left(7-\sqrt{10}\right)\left(7+\sqrt{10}\right)}
Rationalize the denominator of \frac{2}{7-\sqrt{10}} by multiplying numerator and denominator by 7+\sqrt{10}.
\frac{2\left(7+\sqrt{10}\right)}{7^{2}-\left(\sqrt{10}\right)^{2}}
Consider \left(7-\sqrt{10}\right)\left(7+\sqrt{10}\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(7+\sqrt{10}\right)}{49-10}
Square 7. Square \sqrt{10}.
\frac{2\left(7+\sqrt{10}\right)}{39}
Subtract 10 from 49 to get 39.
\frac{14+2\sqrt{10}}{39}
Use the distributive property to multiply 2 by 7+\sqrt{10}.
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