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The phrase "a total strength of around" is correct and usable in written English.
It can be used when discussing an approximate measurement or estimation of strength in a specific context, such as in scientific or technical writing.
Example: "The structure was designed to withstand a total strength of around 5000 Newtons."
Alternatives: "an approximate strength of" or "a total estimated strength of".
Exact(2)
But the rebels have recently gained strength via a well-armed coalition of different factions estimated at a total strength of around 10,000.
On the far right of the French position was a body of light cavalry, consisting of three companies under Des Thermes, Bernadino, and Mauré, with a total strength of around 450 500 men.
Similar(58)
Three unions, claiming a total strength of 600,000 members, say the government has failed to live up to a May settlement.
In all, Drake Force had a total strength of about 720 men.
It became the largest unit in the RAAF, with a total strength of over 1,200.
Serving within the brigade were the 64th Infantry Regiment and the 56th Infantry Regiment, bringing the total strength of the brigade to around 8,000 men.
The latter number seems too high as it would have represented a significant portion of the total strength of Islamic State.
If there is a weakness, then it is the total strength of the squad".
Out of a total votership of around 100,000".
While engaged in anti-partisan work, the battalion grew to a strength of around 1,000.
By June July 1942, the Partisans in eastern Bosnia had been reduced to a strength of around 600 fighters.
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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