cube root
B1Academic / Technical / Everyday Mathematics
Definition
Meaning
The number which, when multiplied by itself twice (i.e., cubed), yields a given number. The operation opposite of cubing.
The value that satisfies the equation x³ = n. More broadly, a concept representing the reverse of a cubic relationship.
Linguistics
Semantic Notes
A specific, unambiguous mathematical term. Always modifies a number (e.g., 'cube root of 8').
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. The term is identical in both varieties.
Connotations
Purely mathematical/technical. No variation in connotation.
Frequency
Frequency is identical, confined to mathematical and educational contexts in both varieties.
Vocabulary
Collocations
Grammar
Valency Patterns
[the] cube root of [number/expression]Vocabulary
Synonyms
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Rare; might appear in financial modelling involving cubic growth.
Academic
Core concept in algebra, calculus, and engineering.
Everyday
Used in basic maths education and practical measurements (e.g., volume).
Technical
Fundamental in mathematics, physics, computer graphics (3D scaling), and engineering.
Examples
By Part of Speech
verb
British English
- To find the volume, you need to cube root the resulting figure.
- Can the software cube root this matrix?
American English
- The function is designed to cube root the input value.
- You'll need to cube root that number to proceed.
adjective
British English
- The cube-root function is continuous.
- We applied a cube-root transformation to the skewed data.
American English
- Use the cube-root key on your calculator.
- The data followed a cube-root relationship.
Examples
By CEFR Level
- The cube root of 27 is 3.
- 8 is a cube number, and its cube root is 2.
- To solve this equation, you must take the cube root of both sides.
- What is the cube root of 64?
- The engineer calculated the cube root of the volume to find the side length of the original cube.
- Unlike square roots, negative numbers have real cube roots.
- Applying a cube-root transformation can help normalise data with a strong right skew.
- The algorithm efficiently computes the cube root of large integers using iterative approximation.
Learning
Memory Aids
Mnemonic
A cube has three dimensions (length, width, height). The cube root 'undoes' the action of creating a 3D cube (cubing).
Conceptual Metaphor
UNRAVELLING A PACKAGE / REVERSING AN ACTION (cubing).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid direct calque 'кубический корень' – the correct term is 'кубический корень' (pronounced koo-bee-che-skiy ko-ren') which is the direct equivalent. No trap.
Common Mistakes
- Confusing it with 'square root'. Forgetting it can be negative for negative numbers (e.g., cube root of -8 is -2). Writing 'cube root' as '³√' incorrectly.
Practice
Quiz
What is the primary conceptual relationship of 'cube root'?
FAQ
Frequently Asked Questions
Yes. Unlike square roots, the cube root of a negative number is also negative (e.g., ∛(-8) = -2), because a negative number cubed stays negative.
In informal technical contexts, it can be verbed ('cube root this value'), but the standard phrasing is 'take the cube root of' or 'find the cube root of'.
The radical symbol with a small 3 (index): ∛. For example, ∛27 = 3.
Square root asks 'what number multiplied by itself gives this?'. Cube root asks 'what number multiplied by itself twice (cubed) gives this?'. Every real number has exactly one real cube root, while only non-negative numbers have real square roots.