The phrase "the approximated" is correct and usable in written English.
You can use it when you want to refer to an estimate or an approximation. For example, "According to the approximated cost, the project will take two months to finish."
Dictionary
the approximated
verb
To carry or advance near; to cause to approach.
Exact(59)
The approximated BER expressions are then formulated.
The expectation of the approximated metric is (33).
The approximated penalty method algorithm allows for efficient parallel computation for sub-problems.
An adaptive sampling technique is used to generate samples and update the approximated LSF.
By solving the model for various values of ε, the approximated Pareto frontier is constructed.
Model validation did not reveal significant differences between the approximated and measured values.
The approximated COG method tracks the position of the saw blade in real-time.
When the approximated coverage is greater than the actual coverage, positions of objects with nonregistered identifications can be estimated within the approximated coverage.
The approximated analytical results given in (36) using (40) and (41).
It shows that the real packet size is larger than the approximated size.
Similar(1)
Correlated standard deviation should be also approximated as the square root of the approximated total covariance value.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com