Evaluate
\frac{-4\sqrt{2}-36}{79}\approx -0.527301953
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\frac{-4\left(9+\sqrt{2}\right)}{\left(9-\sqrt{2}\right)\left(9+\sqrt{2}\right)}
Rationalize the denominator of \frac{-4}{9-\sqrt{2}} by multiplying numerator and denominator by 9+\sqrt{2}.
\frac{-4\left(9+\sqrt{2}\right)}{9^{2}-\left(\sqrt{2}\right)^{2}}
Consider \left(9-\sqrt{2}\right)\left(9+\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{-4\left(9+\sqrt{2}\right)}{81-2}
Square 9. Square \sqrt{2}.
\frac{-4\left(9+\sqrt{2}\right)}{79}
Subtract 2 from 81 to get 79.
\frac{-36-4\sqrt{2}}{79}
Use the distributive property to multiply -4 by 9+\sqrt{2}.
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