<s>[INST] Rationalization of a fraction Can someone please explain how i can rationalize the fraction $\frac{2 +\sqrt{3}}{(2-\sqrt{3})^3}$ so that i obtain an answer that has an exponent of 6. I basically need to compare this value with $\dfrac{(10)^6}{(3)^6}$ to see which is greater. Thanks in advance for helping out!
 [/INST] \begin{align*}
\frac{2+\sqrt{3}}{(2-\sqrt{3})^3}&=\frac{2+\sqrt{3}}{(2-\sqrt{3})^3}\cdot\frac{(2+\sqrt{3})^3}{(2+\sqrt{3})^3}\\
&=\frac{(2+\sqrt{3})^4}{(2^2-3)^3}\\
&=\frac{(2+\sqrt{3})^4}{1}\\
&=(2+\sqrt{3})^4
\end{align*}
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