# What is the origin of "root" as a solution to an equation?

I was curious to know more on the history of the term "root", in the sense of "a value that results in a true statement, when substituted into an equation" (e.g., the roots of $$2x^2 + 1= 9$$ are $$\pm2$$).

I saw this question, which is also about the origin of "root", but in the sense of a zero (i.e., rearranging the previous example into the form $$2x^2 - 8 = 0$$). I'm guessing the answer is the same, although, based on dictionary & encyclopaedic entries, it seems the "valid value" meaning predates the "returns zero" meaning.

Interestingly, Wolframalpha does not even list the "returns zero" meaning in its 14 definitions for "root", despite the fact that Mathematica's "root" function is related to that sense of the word.

The notion of "root" as solution to an equation was simply transferred to this form of writing them, so it has little to do with the "root" as such, as it was previously transferred to general equations from the special case $$x^n=a$$, which explains the name, see Why is the radical symbol √ called "radical"? The word, in its Arabic version jathr, goes back to al-Khwarizmi himself, his famous treatise on algebra (c. 820). Robert of Chester, in his Latin translation Liber algebrae et almucabola (1145), translated jathr as radix. There is even speculation that the first letter in Arabic jathr gave rise to the symbol for root introduced by Rudolff in Europe c. 1525. Recorde in The Whetstone of Witte (1557) translated radix as root, but only as in square root. Although al-Khwarizmi occasionally calls unknowns in equations "jathr" too, see MathForum, this extension did not take in Europe until 17th century; res or cosa were more commonly used.