Class 8MathematicsChapter 7Preksha • Last-Minute Revision
Cubes and Cube Roots
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- A perfect cube has the form n³.
- Prime factors of a perfect cube occur in groups of three.
- Cube of an even number is even; cube of an odd number is odd.
- Cube of a negative number is negative.
- Cube root reverses cubing.
What You Will Learn
- Recognise perfect cubes
- Use basic cube properties
- Find cubes efficiently
- Find cube roots by prime factorisation
- Distinguish square-root pairing from cube-root grouping
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Perfect cubes
A perfect cube is n³. Important values include 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000.
Prime-factor pattern
In the prime factorisation of a perfect cube, each prime occurs with an exponent that is a multiple of 3.
Cube roots
Factor the number into primes, group identical factors in threes and take one factor from each group.
Negative numbers
Odd powers keep the negative sign, so a negative perfect cube has a negative cube root.
Formula Sheet
Formula / Key Relations
Cube
Definition of a cube.
Worked Examples
Cube root
Question
Find cube root of 1728.
Solution
Group prime factors in threes.
Negative cube
Question
Find cube root of -216.
Solution
Because (-6)³ = -216.
Exam Traps
Quick Revision
Quick Revision
- A perfect cube has the form n³.
- Prime factors of a perfect cube occur in groups of three.
- Cube of an even number is even; cube of an odd number is odd.
- Cube of a negative number is negative.
- Cube root reverses cubing.
- Revise the formula sheet once more before attempting questions.
Compact Practice
Q1MCQModerateClass 8
5³?
View Solution
125
Q2MCQModerateClass 8
Cube root of 343?
View Solution
7
Q3ShortModerateClass 8
Is 1000 a perfect cube?
View Solution
Yes, 10³.
Q4ApplicationModerateClass 8
Cube root of -512?
View Solution
-8
Final Chapter Summary
Chapter Summary
- A perfect cube has the form n³.
- Prime factors of a perfect cube occur in groups of three.
- Cube of an even number is even; cube of an odd number is odd.
- Cube of a negative number is negative.
- Cube root reverses cubing.
- Prioritise correct method, clean working and final units where applicable.