square root
Definition
- Noun:
- A number that produces a specified quantity when multiplied by itself: The square root of a number x is a number y such that y × y = x. For example, 3 is the square root of 9 because 3 × 3 = 9.
Usage
- The term "square root" is used to find the original side length from a given area (a square's area is the square of its side length).
- It is commonly represented by the radical symbol (√). For example, √9 = 3.
- Every positive real number has two square roots: one positive (the principal square root) and one negative. For example, both 5 and -5 are square roots of 25.
Examples
- Noun:
- The square root of 16 is 4.
- To solve the equation, you need to calculate the square root of 25.
- In geometry, if a square has an area of 64 square units, the length of its side is the square root of 64, which is 8.
Advanced Usage
- "Principal square root": Refers to the non-negative square root of a non-negative number, denoted by the radical symbol (√). For example, the principal square root of 36 is 6.
- "Imaginary square root": For negative numbers, the square root involves the imaginary unit , where ² = -1. For example, the square root of -4 is 2.
Variants and Related Words
- Root (noun): In mathematics, a more general term. A number that, when raised to a specified power (not just squared), equals a given number (e.g., cube root).
- Radical (noun): The symbol (√) used to denote the square root or other roots.
- Squaring (verb): The inverse operation of finding a square root; multiplying a number by itself.
Synonyms
- Radical (when referring specifically to the square root symbol and its result in context).
Related Phrases
- "Take the square root of": To perform the operation of finding the square root.
- The next step is to take the square root of both sides of the equation.
- "Square root sign": Another term for the radical symbol (√).
- Don't forget to include the square root sign in your answer.
Noun
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a number that when multiplied by itself equals a given number
