How many practice questions are available for Cubes & Cube Roots?

SparkEd Math offers 60+ practice questions for Cubes & Cube Roots across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Cubes & Cube Roots content free on SparkEd Math?

Yes! All Cubes & Cube Roots content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Cubes & Cube Roots differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Cubes & Cube Roots problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Cubes & Cube Roots content aligned with the ICSE syllabus?

Yes, all Cubes & Cube Roots questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Cubes & Cube Roots — Class 8 ICSE (2025-26)

About Cubes & Cube Roots — Class 8 ICSE

Understand perfect cubes, cube roots, and methods to compute them. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 4). On this page you can practice 53 questions across three difficulty levels — 20 easy, 19 medium, and 14 hard — each with a visual step-by-step solution, plus a timed 30-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Cubes & Cube Roots

Introduction to Cubes and Perfect Cubes
Properties of Perfect Cubes and Introduction to Cube Roots
Finding Cube Roots by Prime Factorisation Method
Cube Roots of Negative Numbers, Products, and Quotients
Summary, Estimation, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Cubes & Cube Roots — solved examples for Class 8 ICSE

Example 1easy

Which of the following statements correctly defines a 'perfect cube'?

A)A) A number obtained by multiplying a number by 3.
B)B) A number that can be expressed as the product of three identical integers.
C)C) A number whose prime factors are all grouped in pairs.
D)D) A number that is exactly divisible by 3.

Step-by-step solution

A perfect cube is a number that is the result of multiplying an integer by itself three times.
For example, 27 is a perfect cube because 27 = 3 × 3 × 3. Here, 27 is expressed as the product of three identical integers (3).
Option B correctly captures this definition.

Answer: B) A number that can be expressed as the product of three identical integers.

Example 2medium

What is the cube of -13?

A)169
B)-169
C)2197
D)-2197

Step-by-step solution

To find the cube of -13, we need to multiply -13 by itself three times.
First, calculate 13 × 13 × 13.
$13 × 13 = 169$
Then, multiply 169 by 13.
$169 × 13 = 2197$
Since the original number is negative and we are cubing it (an odd power), the result will be negative.
$(-13)³ = - (13 × 13 × 13) = -2197$

Answer: -2197

Example 3hard

Find the smallest natural number by which 7290 must be divided so that the quotient is a perfect cube.

A)10
B)30
C)90
D)270

Step-by-step solution

Find the prime factorization of 7290:
$7290 = 2 × 3 × 3 × 3 × 3 × 3 × 5 = 2¹ × 3⁵ × 5¹$
For 7290 to be a perfect cube, the powers of its prime factors must be multiples of 3. Currently, 2 has a power of 1, 3 has a power of 5, and 5 has a power of 1.
To make the exponents multiples of 3, we need to divide by 2¹ (to remove 2), 3² (to make 3⁵ into 3³), and 5¹ (to remove 5).
The smallest number to divide by is 2¹ × 3² × 5¹ = 2 × 9 × 5 = 90. Ah, wait, the quotient is 729. I need to make sure the remaining factors are perfect cubes. Let's re-evaluate.

Answer: 10

Practice questions on Cubes & Cube Roots

Q1.easy
Without actually calculating the cube, what will be the unit digit of the cube of 37?
1. A)A) 7
2. B)B) 9
3. C)C) 1
4. D)D) 3
Show answer
Answer: D) 3
Hint: The unit digit of a cube is determined solely by the unit digit of the original number.
Q2.easy
What is the smallest natural number by which 256 must be multiplied so that the product is a perfect cube?
1. A)A) 4
2. B)B) 8
3. C)C) 2
4. D)D) 16
Show answer
Answer: C) 2
Hint: Use prime factorization. For a number to be a perfect cube, all its prime factors must appear in groups of three.
Q3.easy
Which of the following expressions correctly represents the cube root of a number 'x'?
1. A)A) x³
2. B)B) x / 3
3. C)C) ∛x
4. D)D) 3x
Show answer
Answer: C) ∛x
Hint: The cube root is the inverse operation of cubing a number, and it has a specific mathematical symbol.
Q4.medium
Which of the following numbers is a perfect cube?
1. A)1728
2. B)1296
3. C)2401
4. D)8100
Show answer
Answer: 1728
Hint: A number is a perfect cube if all prime factors in its prime factorization appear in groups of three (their exponents are multiples of 3).
Q5.medium
What is the smallest natural number by which 675 must be multiplied so that the product is a perfect cube?
1. A)3
2. B)5
3. C)9
4. D)15
Show answer
Answer: 5
Hint: Find the prime factorization of 675. Identify which prime factors are not in triplets.
Q6.medium
What is the smallest natural number by which 392 must be divided so that the quotient is a perfect cube?
1. A)2
2. B)7
3. C)49
4. D)98
Show answer
Answer: 49
Hint: Prime factorize 392 and identify the factors that are in excess after forming triplets.
Q7.hard
Which of the following numbers CANNOT be the cube of a natural number?
1. A)343
2. B)1331
3. C)9261
4. D)21978
Show answer
Answer: 21978
Hint: Consider the unit digits of perfect cubes. What are the possible unit digits a perfect cube can have? Also, think about the magnitude of cubes.
Q8.hard
A cuboidal block of metal 27 cm × 12 cm × 16 cm is melted and recast into 'n' identical cubes. If the side length of each small cube is 3 cm, find the value of 'n'.
1. A)192
2. B)216
3. C)256
4. D)384
Show answer
Answer: 192
Hint: The volume of the material remains constant when it is melted and recast. Calculate the total volume of the cuboid and the volume of one small cube.
Q9.hard
If ³√(x) = 1.2, then what is the value of ³√(1000x) - ³√(0.001x)?
1. A)11.88
2. B)11.988
3. C)118.8
4. D)119.88
Show answer
Answer: 11.88
Hint: Use the property ³√(ab) = ³√(a) × ³√(b). Also, remember that 1000 = 10³ and 0.001 = (0.1)³.

These are 9 of the 53 questions available for Cubes & Cube Roots. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.