From the time of the first calculators, the fundamental question in all of school mathematics from primary to tertiary level has been what to do about paper and pencil skills in a calculator/computer age. (See Usiskin (1998).)
In the United States, the hand calculation of square roots was taken out of textbooks almost immediately after the appearance of the first hand-held calculators. Few have missed it. Some mathematicians today want the hand calculation of square roots to return, but it will not except as a mathematical curiosity or historical artifact.