Evaluate
\sqrt{2}+\sqrt{7}\approx 4.059964873
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\frac{5\left(\sqrt{7}+\sqrt{2}\right)}{\left(\sqrt{7}-\sqrt{2}\right)\left(\sqrt{7}+\sqrt{2}\right)}
Rationalize the denominator of \frac{5}{\sqrt{7}-\sqrt{2}} by multiplying numerator and denominator by \sqrt{7}+\sqrt{2}.
\frac{5\left(\sqrt{7}+\sqrt{2}\right)}{\left(\sqrt{7}\right)^{2}-\left(\sqrt{2}\right)^{2}}
Consider \left(\sqrt{7}-\sqrt{2}\right)\left(\sqrt{7}+\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{5\left(\sqrt{7}+\sqrt{2}\right)}{7-2}
Square \sqrt{7}. Square \sqrt{2}.
\frac{5\left(\sqrt{7}+\sqrt{2}\right)}{5}
Subtract 2 from 7 to get 5.
\sqrt{7}+\sqrt{2}
Cancel out 5 and 5.
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