Evaluate
\frac{8\left(\sqrt{10}-5\right)}{15}\approx -0.980118581
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\frac{-8\left(5-\sqrt{10}\right)}{\left(5+\sqrt{10}\right)\left(5-\sqrt{10}\right)}
Rationalize the denominator of \frac{-8}{5+\sqrt{10}} by multiplying numerator and denominator by 5-\sqrt{10}.
\frac{-8\left(5-\sqrt{10}\right)}{5^{2}-\left(\sqrt{10}\right)^{2}}
Consider \left(5+\sqrt{10}\right)\left(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{-8\left(5-\sqrt{10}\right)}{25-10}
Square 5. Square \sqrt{10}.
\frac{-8\left(5-\sqrt{10}\right)}{15}
Subtract 10 from 25 to get 15.
\frac{-40+8\sqrt{10}}{15}
Use the distributive property to multiply -8 by 5-\sqrt{10}.
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