# Root extraction

The need for action, exponentiation, and root extraction was caused by a practical need. Since ancient times, people have solved the problem: "find the length of the side of the square, if its area is known". Another 4000 years ago, the Babylonian scholars compiled tables of squares of numbers. In doing so, they were able to find approximate values for extracting the square root from any integer. But economic needs have long forced people to calculate not only the area of the figures, but also the volumes of different bodies. One of the most ancient tasks, probably, was the task: "What should be the length of the edge of the cube, so that its volume is equal to a?" The task leads to extracting the root of the cube from a. Among the famous tasks that the ancient Greek scholars were still in the 5th and 4th centuries, BC, was task about doubling the cube: "find the edge of the cube, whose volume is twice the volume of this cube". Methods of extracting the root of a cubic and a square with the help of a counting board and counting sticks are contained in the Chinese treatise of the 13th century. "Mathematics in nine books". The Greek mechanic and mathematician Geron of Alexandria (1st century AD), who did much for the development of computational and applied mathematics, gave a scheme for the approximate extraction of cubic roots.

The word "root" (square or root of the equation) came from the Arabs. Arab scholars imagined the square of a number rising from the root, like a plant; hence the name - the root (or radix - from the Latin radix). By the way, the "traces" of this word can still be found in the words "radish", "radish".

Since the 13th century, Italian and other European mathematicians have designated the extraction of the root by the Latin word "radix" or abbreviated Rx. The modern sign of root extraction originated from the notation used by German mathematicians of the 15th and 16th centuries, who called algebra "spit", and algebraists "cossists". Some German 15th century cossiers denoted the square root as a point ahead of the number or expression; roots of higher degrees - several points. Of the points placed before the subradical numbers that passed into the cursive line in the dashes, there probably appeared a root sign (without the top dash). This sign (V) occurs for the first time in the German algebra "A quick and beautiful account using the clever rules of algebra", published in 1525 in Strasbourg. The author of this book was a native of the Czech Republic, a mathematics teacher in Vienna, Kshitof Rudolph from Yavor. The book was a success and was republished during the 16th century and up to 1615. In 1626 the Dutch mathematician A. Girard introduced the notation V, W, VW to extract the square, cubic and greater roots. If the figure was above this sign, then this meant extracting the square root, if 3 is cubic. This designation displaces the sign of Rx.

R. Descartes connected the root extraction to the horizontal bar, using in his "Geometry" (1637) a modern sign of extracting the root. This sign came into general use only in the early 18th century. In the 18th century it was found that the square root of a positive number has two values - positive and negative, and it is impossible to extract a square root from a negative number.