Time for Numbers

Let a rational number be $R= \dfrac pq$ . Here, $p$ is not divisible by $q \Rightarrow p^2$ is not divisible by $q^2.$

Squaring, $R^2 = \dfrac {p^2}{q^2} = \dfrac pq \times \dfrac pq \neq Z$ Here, $Z$ is any integer.

Hence , $\boxed{NO}.$

All rational numbers can be written in the form $\frac{x}{y}$ where $y \neq 0$ and both x and y are integers. We're going to write our original number in this format.

Since our number isn't an integer, even with our fraction in simplest form, $y \neq 1$ .

When we multiply our fraction by itself, cross multiplying isn't possible since the fraction is already in simplest form.

After multiplying two fractions in simplest form and finishing cross multiplying, if possible (which is wasn't in this case), our result is in simplest form.

Since y wasn't equal to 1, the new fraction's denominator can't be 1 either, and the only possibility for a fraction in simplest form to be an integer is for its denominator to be 1, which we just proved impossible.

Therefore, the answer is $\boxed {No}$ .