Q1.
Why is the word ‘root’ (the root of a plant) used for the mathematical operation √ (square root, cube root, etc.)?
Answer
Because the Sanskrit word mula — the root of a plant, and also basis, cause, origin — was the term ancient Indian mathematicians used for this operation.
- varga = square (the figure, its area, and the second power); varga-mula = square root.
- ghana = cube (the solid and the third power); ghana-mula = cube root.
- pada (foot, basis, origin) was another word for root. Brahmagupta (628 CE) writes, "The pada (root) of a krti (square) is that of which it is a square."
Why the image fits: A root is what a thing grows out of. The number 3 is what 9 "grows from" when it is squared, so calling 3 the root of 9 is the same picture as a plant growing from its root. The word travelled: Arabic took jidhr and Latin took radix, both meaning the root of a plant, and English "root" and "radical" come from the Latin.
Did you know? Mula in this mathematical sense has been used in India since at least the first century BCE, and varga and ghana since at least the third century BCE. The fourth power had its own name, varga-varga — square of the square.