square root: meaning, definition, pronunciation and examples
C1Technical/Academic
Quick answer
What does “square root” mean?
A number which, when multiplied by itself (squared), produces a specified number. For example, 3 is the square root of 9 because 3 × 3 = 9.
Audio
Pronunciation
Definition
Meaning and Definition
A number which, when multiplied by itself (squared), produces a specified number. For example, 3 is the square root of 9 because 3 × 3 = 9.
Used metaphorically to denote a fundamental source, cause, or basis from which something originates or is derived.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or semantic differences. Potential minor variation in the pronunciation of 'root' (/ruːt/ vs. /rʊt/ or /rut/).
Connotations
Identical technical connotations in both varieties.
Frequency
Equally frequent in mathematical/technical contexts in both varieties.
Grammar
How to Use “square root” in a Sentence
[The] square root of [NUMBER]Find/calculate [the] square rootVocabulary
Collocations
Examples
Examples of “square root” in a Sentence
verb
British English
- To solve this, you need to square-root both sides of the equation.
- The function square-roots the input value.
American English
- We'll need to square root that value in the next step.
- The software square roots the data automatically.
adjective
British English
- Use the square-root key on your calculator.
- We applied a square-root transformation to the data.
American English
- The square-root function is on the calculator.
- A square-root transformation normalized the dataset.
Usage
Meaning in Context
Business
Virtually never used, except in highly specialised financial modelling or analytics.
Academic
Core term in mathematics, physics, engineering, and statistics education and research.
Everyday
Limited to basic maths discussions (e.g., helping with homework) or humorous/sarcastic metaphorical use (e.g., 'He's the square root of all our problems').
Technical
Fundamental and frequent concept in pure and applied mathematics, computer science, and engineering.
Vocabulary
Synonyms of “square root”
Neutral
Weak
Vocabulary
Antonyms of “square root”
Watch out
Common Mistakes When Using “square root”
- Using 'square root' to mean 'divided by two'.
- Forgetting the negative square root when solving equations (e.g., x² = 9 has solutions x = 3 and x = -3).
- Incorrect collocation: 'square root from 16' instead of 'square root of 16'.
FAQ
Frequently Asked Questions
Yes, but not a real number. The square root of a negative number is an imaginary number, denoted with the imaginary unit i (e.g., √-4 = 2i).
Squaring a number means multiplying it by itself (e.g., 5 squared is 25). Finding a square root is the inverse operation (e.g., the square root of 25 is 5).
Because both a positive and a negative number, when multiplied by themselves, yield the same positive result (e.g., 3×3=9 and (-3)×(-3)=9).
No, √2 is an irrational number. It cannot be expressed as a simple fraction, and its decimal representation goes on forever without repeating.
A number which, when multiplied by itself (squared), produces a specified number. For example, 3 is the square root of 9 because 3 × 3 = 9.
Square root is usually technical/academic in register.
Square root: in British English it is pronounced /skweə ruːt/, and in American English it is pronounced /skwɛr rut/ or /skwɛr rʊt/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Imagine a square garden. To find its area, you multiply the side length by itself. To find the side length from the area, you need the square *root* that grew that area.
Conceptual Metaphor
FOUNDATION/SOURCE (The square root is the foundational element that, when combined with itself, builds the original number.)
Practice
Quiz
Which of the following is the correct mathematical notation for the square root of 25?