Answer
No, the process of squaring the radical is not equivalent to rationalizing the denominator.
Work Step by Step
Lets perform both squaring and rationalizing of the denominator and see if we get the same result.
\begin{equation}
\begin{aligned}
\left(\frac{2}{\sqrt{3}} \right)^2&= \frac{4}{3}\\
\frac{2}{\sqrt{3}} & =\frac{2}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}\\
& =\frac{2\sqrt{3}}{3}\\
\end{aligned}
\end{equation}
Clearly, the results are different. Rationalizing the denominator only eliminates the radical from the denominator. without changing the value of the initial number while squaring an irrational number changes its value.
