161. Does the liberation of fractions from irrationality in the denominator have any other purpose besides providing an excuse for exercises?

Does the removal of irrationality from the denominator of fractions serve any other purpose besides offering a pretext for exercises?
161. If it is required to calculate the approximate value of an expression containing irrational numbers (radicals) in the denominator, then division by a multi-digit decimal is quite inconvenient; it is also not easy to determine the degree of approximation (error); for example, instead of

$$
\frac{1}{\sqrt{2}}=\frac{1}{1.4142}=\frac{10000}{14142}
$$

it is much simpler to perform the following calculation:

$$
\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}=\frac{1.4142}{2}
$$

Thus, freeing from irrationality in the denominator can have significant practical value.