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The phrase "approximated the size" is correct and usable in written English.
It can be used when discussing measurements or estimations in various contexts, such as scientific research, engineering, or general descriptions.
Example: "The researchers approximated the size of the asteroid based on its brightness and distance from Earth."
Alternatives: "estimated the size" or "calculated the size".
Exact(7)
Full weight bearing without a cast was allowed when graft hypertrophy matched or approximated the size of the shaft of the tibia.
The resultant gap was filled with copper tokens that approximated the size of the halfpenny, struck on behalf of merchants.
The Tang census of 742 again approximated the size of China's population at about 50 million people.
As the half eagle approximated the size of a number of foreign gold coins, such as the British guinea and the French louis d'or, it was accepted readily in international commerce and was of a suitable value for many business transactions.
The spatial domain, comprised of 76 (37.5 km × 37.5 km) unit squares, approximated the size and scale of South Korea.
This shift approximated the size difference between pYHCC and pXZ, and further suggested pXZ as the origin of pYHCC.
Similar(53)
Probably the best bet is lobsters, from four pounds to creatures approximating the size of those kiddie automobiles sold at F. A. O. Schwarz.
These two designs were presented to users on two screen sizes; a larger size approximating the size of a standard laptop or desktop screen and a smaller size approximating the size of a PDA screen.
Signers Hall, where the bronzes will be displayed, is a soaring space, 24 feet high and 37 feet square, which approximates the size of the Assembly Room in Independence Hall two blocks away, where the Constitution was written and signed.
ERMA controlled two of the Check Reader/Sorters, each approximating the size of a Ford Explorer.
The 2500 feet by 2500 feet grid cell approximates the size of the average block-group in Cincinnati.
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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