Talk:Square root

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Difference between “Quadratwurzel” and “square root”

Hello everyone,

At this point I would like to draw attention to a terminological difference that exists between German (and perhaps other languages) and English regarding the term “square root”.

In English the question "What is the square root of 16?" be understood as asking about the “roots” of the quadratic equation x² = 16.

In German, no one would talk about the “Wurzeln” (“roots”) of a quadratic equation, but only about the “Lösungen” (“solutions”) of a quadratic equation. The question “Was ist die Quadratwurzel von 16?” (“What is the square root of 16?”) is always understood in German to mean asking for the result of √(16).

This means: In German we only speak of “Quadratwurzel” (“square root”) when we speak of “principal square root” in English. That is, the German term “Quadratwurzel” refers exclusively to this sign: √ (or to something with the exponent ½).

If someone from Germany only reads the opening text of this article, this someone will get a completely wrong idea of what a “Quadratwurzel” is in German. That’s why I would like to ask you to address the meaning of “principal square root” right at the beginning of the text and to say that in languages like German, the term “square root” is used in the sense of “principal square root”.

Please read also the German Wikipedia article “Quadratwurzel”.

Best regards -- Jake2042 (talk) 20:15, 24 August 2024 (UTC)[reply]

The article says explicitly that "the square root" of a nonnegative number is its positive square root, and that ⁠

{\sqrt {16}}

⁠ denotes only the positive square root.

What you say of German usage seems to mean that "Quadratwurzel" is not used for complex numbers; this is unbelievable. D.Lazard (talk) 21:26, 24 August 2024 (UTC)[reply]

@Jake2042: This page is for discussions related to work on the corresponding article; it is not a general web forum for discussing other, albeit related, matters, such as differences between usages in different languages. However, for what it may be worth to you, here are just a few German language sources which use the word "Quadratwurzel" referring to roots of complex numbers: 1, 2, 3. There are many more. JBW (talk) 10:46, 25 August 2024 (UTC)[reply]

Typo?

Guys there is a small typo in this section of the first paragraph "The term (or number) whose square root is being considered is known" — Preceding unsigned comment added by 202.63.79.208 (talk) 13:21, 26 September 2024 (UTC)[reply]

What typo is that? I can't see a typo. JBW (talk) 21:16, 28 September 2024 (UTC)[reply]

Computation

should be references to CORDIC algorithm for how to compute square root in scientific calculators and microprocessors etc. 88.89.57.3 (talk) 14:34, 28 September 2024 (UTC)[reply]

z¹ᐟ² is not principal root, z¹ᐟ² = ±√z, not just √z.

Let z = r²e^iθ (r≥0)

z = r²e^iθ = r²e^i(θ+2kπ) (∀k∈ℤ)

⇔ z¹ᐟ² = {r²e^i(θ+2kπ)}¹ᐟ² ⇔ z¹ᐟ² = re^i(θ/2+kπ) = ±re^(iθ/2) = ±√z. KarlTWilson (talk) 20:39, 16 November 2024 (UTC)[reply]