平方根（へいほうこん、heihoukon）
- square root

The Japanese word 平方根 （へいほうこん） means "square root". It refers to a value that, when multiplied by itself, gives the original number. In other words, it's the inverse operation of squaring a number. For example, the 平方根 of 9 is 3 because 3 multiplied by 3 (3²) equals 9. It's important to note that a positive number usually has two square roots: a positive one and a negative one. For instance, both 3 and -3 are 平方根s of 9. This concept is fundamental in mathematics and is used in various fields like geometry, physics, and engineering.

⚫︎ 9の平方根 Translation: The square root of 9. ⚫︎ 4の平方根は2と-2です。 Translation: The square roots of 4 are 2 and -2. ⚫︎ 平方根を計算する。 Translation: Calculate the square root.

You would use 平方根 when discussing mathematical concepts, particularly when dealing with equations, geometric calculations (like finding the side length of a square given its area), or in any context involving the reverse of the squaring operation. It's a technical term, so it's not commonly used in everyday casual conversation unless the subject is mathematics or a related field. You might encounter it in textbook problems or when explaining mathematical principles.

平方根 is typically written using the kanji 平方根, but it’s sometimes written in hiragana as へいほうこん, especially for learners. The okurigana (the suffix hiragana) is standard and doesn't have variations.

There aren't many direct synonyms in Japanese. However, you could use phrases that describe the concept, such as 2乗の逆演算 (the inverse operation of squaring) in a descriptive manner.

The direct antonym is the square itself, which is expressed as 2乗 or 二乗 （にじょう）, meaning "squared".

この図形の面積が25cm²のとき、一辺の長さは平方根を使って求められます。 ・Translation: When the area of this figure is 25 cm², the length of one side can be found using the square root. ・Explanation: This sentence illustrates the application of 平方根 in geometry, specifically finding a side length given the area of a square.

√16の平方根は4です。 ・Translation: The square root of √16 is 4. ・Explanation: This clarifies that the 平方根 of the square root of 16 (which is 4) is 4.

The word 平方根 is a compound word. 平方 （へいほう） means "square" (referring to a number multiplied by itself). 根 （こん） literally means "root," in this context, it refers to the root of a number, the value that produces a given number when multiplied by itself. Therefore, 平方根 is a direct translation of the mathematical concept of "square root".