radical sign

Thân thiện

A student writes a radical sign on the chalkboard.

Definition

1. Noun:
   • A mathematical symbol (√) placed before a number or expression to indicate that its root (typically the square root) is to be taken: The radical sign is the principal symbol used to denote the operation of finding a root of a quantity.

Usage

• The radical sign is used in arithmetic and algebra.
• It is placed directly before the radicand (the number or expression under the root).
• For roots other than the square root, a small index number is placed in the "v" of the radical sign (e.g., ³√ for cube root).

Examples

• Noun:
  • The equation required us to simplify the expression under the radical sign.
  • To solve for x, you must first isolate the term containing the radical sign.
  • The radical sign √16 indicates the principal (non-negative) square root of 16, which is 4.

Advanced Usage

• "Nth root radical sign": When a small number is included, it specifies the degree of the root (e.g., the cube root radical sign is written as ³√).
• "Radical sign with vinculum": The horizontal line extending over the radicand is called a vinculum; it groups the terms to which the root applies.

Variants and Related Words

• Radical (n): The entire expression consisting of the radical sign and the radicand.
• Radicand (n): The number or expression inside the radical sign, under the vinculum.
• Square root symbol: A common name for the radical sign (√) when no index is written, implying an index of 2.

Synonyms

• Root symbol: A more general term.
• Surd symbol: A less common term, historically used, especially for irrational roots.

Notes

• The radical sign is distinct from the notation using fractional exponents (e.g., x^(1/2) is equivalent to √x).
• In computer notation and some texts, the function is often used instead of the radical sign.

Học thuật

Noun

1. a sign indicating the extraction of a root