Class 8 Maths - ICSE
Cubes and Cube Roots (ICSE)
The chapter Cubes and Cube Roots for Class 8 ICSE builds directly upon the concepts of squares and square roots, introducing students to three-dimensional multiplication. You will learn how to identify perfect cubes, find cube roots using prime factorisation and estimation methods, and apply these concepts to solve word problems involving volume. In ICSE board exams, this topic is a high-scoring foundational area, frequently appearing in both objective and short-answer sections. Mastering this chapter not only secures crucial marks in your Class 8 finals but also strengthens your calculation speed and number sense for higher-level algebra in Class 9 and 10.
Start Learning FreeKey Concepts
Cube of a Number
The cube of a number is obtained by multiplying the number by itself three times, denoted as a³ = a × a × a.
Perfect Cube
A natural number is called a perfect cube if it is the cube of some natural number, such as 1, 8, 27, 64, and so on.
Cube Root
The cube root of a number is the factor that we multiply by itself three times to get that number, denoted by the symbol ∛.
Prime Factorisation Method
A method to find the cube root of a number by breaking it into prime factors and grouping them in triplets.
Properties of Cubes
Cubes of even numbers are always even, cubes of odd numbers are always odd, and negative numbers always have negative cubes.
Important Formulas
Board Exam Info
In the ICSE Class 8 Mathematics examination, this chapter typically carries around 4 to 6 marks. Common question types include checking whether a given number is a perfect cube, finding the smallest number by which a number must be multiplied or divided to make it a perfect cube, calculating cube roots using prime factorisation, and solving word problems based on the volume of cubical objects.
Frequently Asked Questions
How can I quickly find out if a large number is a perfect cube without full division?
You can use the prime factorisation method. If all the prime factors of the number can be successfully grouped into exact triplets of identical numbers, then it is a perfect cube.
What is the difference between square root and cube root?
A square root finds a number that multiplies by itself twice to give the original number, whereas a cube root finds a number that multiplies by itself three times.
Can negative numbers have cube roots?
Yes, negative numbers have real cube roots. For example, the cube root of -27 is -3 because (-3) × (-3) × (-3) = -27.
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