In an era where smartphones are used daily by schoolchildren, wanting to extract a square root might seem "old-fashioned"…
However, in France, this technique was taught in primary school until about the 50s/60s. At present, the pupils, arriving in sixth grade, still have difficulties in establishing a division. Through my long online teaching trips, discovering students in the four corners of the globe, I was able to confront myself with other types of teaching and presentation of mathematics.As a lifetime learner, I have rejuvenated myself by listening to them and trying to create aids for the understanding of their courses. This technique remains taught in some countries of Africa and Asia where the calculator remains mostly prohibited for exams whether in mathematics or physical sciences.
We find the detailed technique in the manual "The second year of arithmetic" of P.Lesseynne. This manual is available online on the BNF website.
I explain the method here in video using several examples. The infographic, below, will allow you to visualize each step.