Evaluate
-\left(\sqrt{5}+\sqrt{10}\right)\approx -5.398345638
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\frac{5\left(\sqrt{5}+\sqrt{10}\right)}{\left(\sqrt{5}-\sqrt{10}\right)\left(\sqrt{5}+\sqrt{10}\right)}
Rationalize the denominator of \frac{5}{\sqrt{5}-\sqrt{10}} by multiplying numerator and denominator by \sqrt{5}+\sqrt{10}.
\frac{5\left(\sqrt{5}+\sqrt{10}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{10}\right)^{2}}
Consider \left(\sqrt{5}-\sqrt{10}\right)\left(\sqrt{5}+\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{5\left(\sqrt{5}+\sqrt{10}\right)}{5-10}
Square \sqrt{5}. Square \sqrt{10}.
\frac{5\left(\sqrt{5}+\sqrt{10}\right)}{-5}
Subtract 10 from 5 to get -5.
-\left(\sqrt{5}+\sqrt{10}\right)
Cancel out -5 and -5.
-\sqrt{5}-\sqrt{10}
To find the opposite of \sqrt{5}+\sqrt{10}, find the opposite of each term.
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