The square root of a number was a second number that when multiplied by itself once became the first number.
Calculating the square root was a common and useful albeit boring and complex mathematical operation. For example, Data once told a very boring "anecdote" about how he calculated the square root of pi as a way of determining the distance between two stellar objects. (TNG: "Manhunt")
During a Ferengi takeover of the Enterprise in 2369, William Riker succeeded in confusing a Ferengi which had ordered him to explain the computer by spewing overtly complex and confusing information. Among his claims were that the ramistat kiloquad capacity was a function of the square root of the intermix ratio times the sum of the plasma injector quotient. (TNG: "Rascals")
In 2373, while Odo and Quark were stranded on an uninhabited planet and forced to ascend to higher terrain, Quark estimated the height of a mountain saying "carry the seven, take the square root, times pi". His result was that the mountain was "high". (DS9: "The Ascent")