The main point is that the ages of rock formations are rarely based on a single, isolated age measurement.
On the contrary, radiometric ages are verified whenever possible and practical, and are evaluated by considering other relevant data.
They observed that every rock formation, no matter how ancient, appeared to be formed from still older rocks.
Comparing these rocks with the products of present erosion, sedimentation, and earth movements, these earliest geologists soon concluded that the time required to form and sculpt the present Earth was immeasurably longer than had previously been thought.
The discovery of radioactivity in 1896 by Henri Becquerel, the isolation of radium by Marie Curie shortly thereafter, the discovery of the radioactive decay laws in 1902 by Ernest Rutherford and Frederick Soddy, the discovery of isotopes in 1910 by Soddy, and the development of the quantitative mass spectrograph in 1914 by J. Thomson all formed the foundation of modern isotopic dating methods.
But it was not until the late 1950s that all the pieces were in place; by then the phenomenon of radioactivity was understood, most of the naturally occurring isotopes had been identified and their abundance determined, instrumentation of the necessary sensitivity had been developed, isotopic tracers were available in the required quantities and purity, and the half-lives of the long-lived radioactive isotopes were reasonably well known.
The point is that not all methods are applicable to all rocks of all ages.
One of the primary functions of the dating specialist (sometimes called a geochronologist) is to select the applicable method for the particular problem to be solved, and to design the experiment in such a way that there will be checks on the reliability of the results.
For example, a method based on a parent isotope with a very long half-life, such as C method can only be used to determine the ages of certain types of young organic material and is useless on old granites.
Some methods work only on closed systems, whereas others work on open systems.
Second, the rock or mineral must not lose or gain either potassium or argon from the time of its formation to the time of analysis.