Cube and Cube Roots class 8- NCERT Concept & Practice Questions

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Radhika SharmaI am a dedicated mathematics educator with 5 years of experience teaching students in both online and offline classrooms. With a Master’s degree in Mathematics and a Bachelor’s in Education, I focus on helping children understand concepts logically instead of memorising them. I am passionate about creating clear, engaging, and student friendly learning experiences that build confidence in mathematics.

Last Updated At: 24 Mar 2026

11 min read

Table of Contents

What is a Cube?
List of Perfect Cubes (1 to 20)
What is a Cube Root?
Finding Cube Roots by Estimation Method
Identifying Perfect Cubes
NCERT-Based Solved Questions
Practice Questions You Should Try
Tricks to Remember Cubes and Cube Roots Easily
Common Mistakes Students Make in Cube and Cube Roots
Shortcut Methods to Solve Cube Root Questions Faster
Importance of Cube and Cube Roots in Higher Classes
PlanetSpark: Make Math Learning Simple and Fun
Conclusion

Have you ever wondered how architects calculate the volume of a cube-shaped water tank or how games design 3D objects so precisely? The answer lies in a simple yet powerful concept you learn in Class 8 and cube and cube roots.

Understanding cubes isn’t just about solving math problems but it’s about visualizing the world in three dimensions. Whether it's packaging boxes, building structures, or even coding 3D models, cube concepts play a crucial role.

In this blog, we’ll break down the NCERT Class 8 cube and cube roots chapter in a simple, conversational way. We’ll also include easy explanations, tricks, solved examples, and practice questions to help you master the topic confidently.

What is a Cube?

A cube of a number is the result of multiplying the number by itself three times.

Formula:

\text{Cube of a number} = n^3 = n \times n \times n

$Cube of a number$ $=$ $n$ $3$ $=$ $n$ $\times$ $n$ $\times$ $n$

Examples:

$2^3 = 2 \times 2 \times 2 = 8$ $2$ $3$ $=$ $2$ $\times$ $2$ $\times$ $2$ $=$ $8$
$3^3 = 3 \times 3 \times 3 = 27$ $3$ $3$ $=$ $3$ $\times$ $3$ $\times$ $3$ $=$ $27$
$5^3 = 125$ $5$ $3$ $=$ $125$

Key Points:

Cube is always a perfect cube if it comes from multiplying the same number thrice.
Cubes can be positive or negative:
- $(-3)^3 = -27$ $($ $-3$ $)$ $3$ $=$ $-27$

List of Perfect Cubes (1 to 20)

Memorizing these helps solve problems faster:

Number	Cube
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000
11	1331
12	1728
13	2197
14	2744
15	3375
16	4096
17	4913
18	5832
19	6859
20	8000

What is a Cube Root?

The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Symbol:

\sqrt[3]{n}

$3$ $n$ $$

Examples:

$\sqrt[3]{8} = 2$ $3$ $8$ $$ $=$ $2$
$\sqrt[3]{27} = 3$ $3$ $27$ $$ $=$ $3$
$\sqrt[3]{125} = 5$ $3$ $125$ $$ $=$ $5$

Important Note:

Cube root of a negative number is also negative:
- $\sqrt[3]{-27} = -3$ $3$ $-27$ $$ $=$ $-3$

Real-Life Applications of Cubes

Volume of a cube: $side^3$ $side$ $3$
Packaging boxes
3D graphics and gaming
Architecture and construction

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Finding Cube Roots by Prime Factorization

This is one of the most important methods in NCERT.

Steps:

Find prime factors of the number
Group them in triples
Multiply one number from each group

Example:

Find cube root of 216

216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3

$216$ $=$ $2$ $\times$ $2$ $\times$ $2$ $\times$ $3$ $\times$ $3$ $\times$ $3$

Group:

(2 \times 2 \times 2)(3 \times 3 \times 3)

$($ $2$ $\times$ $2$ $\times$ $2$ $)$ $($ $3$ $\times$ $3$ $\times$ $3$ $)$

Cube root:

2 \times 3 = 6

$2$ $\times$ $3$ $=$ $6$

Finding Cube Roots by Estimation Method

Useful for large numbers.

Example:

Find cube root of 4913

Step 1: Look at last digit

4913 ends with 3 → cube root ends with 7

Step 2: Remove last 3 digits

Remaining number: 4

Step 3: Find nearest cube

$1^3 = 1$ $1$ $3$ $=$ $1$ , $2^3 = 8$ $2$ $3$ $=$ $8$
4 lies between → choose smaller → 1

Final Answer:

\sqrt[3]{4913} = 17

$3$ $4913$ $$ $=$ $17$

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Properties of Cubes

1. Cube of Even Number

Always even
Example: $4^3 = 64$ $4$ $3$ $=$ $64$

2. Cube of Odd Number

Always odd
Example: $5^3 = 125$ $5$ $3$ $=$ $125$

3. Cube of Negative Number

Always negative
Example: $(-2)^3 = -8$ $($ $-2$ $)$ $3$ $=$ $-8$

4. Perfect Cubes Have Specific Patterns

Ending digits follow patterns:
- 1 → 1
- 2 → 8
- 3 → 7
- 4 → 4
- 5 → 5
- 6 → 6
- 7 → 3
- 8 → 2
- 9 → 9
- 0 → 0

Identifying Perfect Cubes

A number is a perfect cube if:

Prime factors can be grouped in triples
Cube root is a whole number

Example:

Is 72 a perfect cube?

72 = 2^3 \times 3^2

$72$ $=$ $2$ $3$ $\times$ $3$ $2$

Since 3 is not in a group of 3 → Not a perfect cube

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NCERT-Based Solved Questions

Q1. Find cube of 12

12^3 = 1728

$12$ $3$ $=$ $1728$

Q2. Find cube root of 343

\sqrt[3]{343} = 7

$3$ $343$ $$ $=$ $7$

Q3. Is 1331 a perfect cube?

1331 = 11^3

$1331$ $=$ $11$ $3$

Yes, it is a perfect cube.

Q4. Find cube root of 1000

\sqrt[3]{1000} = 10

$3$ $1000$ $$ $=$ $10$

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Practice Questions You Should Try

Easy Level

Find cube of 6
Find cube of 9
Find cube root of 512
Find cube root of 64

Medium Level

Is 216 a perfect cube?
Find cube root of 2744
Find cube of 15
Find cube root of 729

Advanced Level

Find smallest number to multiply 72 to make it a perfect cube
Find cube root of 17576
Express 8000 as cube of a number
Find cube root of 46656

Answers to Practice Questions

216
729
8
4
Yes
14
3375
9
Multiply by 3 → 216
26
$20^3$ $20$ $3$
36

Tips to Master Cube and Cube Roots

Memorize cubes from 1 to 20
Practice prime factorization regularly
Learn digit patterns for quick estimation
Solve NCERT exercises multiple times

Common Mistakes to Avoid

Confusing square with cube
Incorrect grouping in factorization
Ignoring negative signs
Guessing cube roots without logic

Tricks to Remember Cubes and Cube Roots Easily

Learning cubes doesn’t always have to be about rote memorization. With a few smart tricks, students can quickly recall values and solve problems faster during exams.

One of the easiest ways is to learn cubes through patterns. For example, numbers ending in 1, 4, 5, 6, 9, and 0 retain the same unit digit when cubed. This helps in quickly identifying cube roots during estimation.

Another useful trick is to break numbers into smaller parts. For instance, instead of calculating $13^3$ $13$ $3$ directly, you can use:

(10 + 3)^3

$($ $10$ $+$ $3$ $)$ $3$

This makes calculations simpler and faster.

Also, repetition and visualization play a key role. Try visualizing cubes as 3D boxes this not only helps in understanding volume but also strengthens memory.

Lastly, practice regularly using mental math techniques. The more you practice, the easier it becomes to recall cubes instantly without hesitation.

Word Problems Based on Cube and Cube Roots

Word problems are important because they test your understanding of concepts in real-life situations.

Example 1:

A cube-shaped box has a side of 5 cm. What is its volume?

Volume = side^3 = 5^3 = 125 \, cm^3

$Volume$ $=$ $side$ $3$ $=$ $5$ $3$ $=$ $125$ $cm$ $3$

Example 2:

A cube has a volume of 729 cm³. Find its side.

\sqrt[3]{729} = 9

$3$ $729$ $$ $=$ $9$

So, the side of the cube is 9 cm.

Example 3:

How many small cubes of side 1 cm can fit into a cube of side 10 cm?

10^3 = 1000

$10$ $3$ $=$ $1000$

So, 1000 small cubes can fit inside.

These types of questions are commonly asked in exams, so practicing them improves both speed and accuracy.

Common Mistakes Students Make in Cube and Cube Roots

Even though this chapter is considered scoring, students often lose marks due to small but avoidable mistakes. Being aware of these can significantly improve accuracy.

One common mistake is confusing cubes with squares. For example, students sometimes calculate $5^3$ $5$ $3$ as $5 \times 5 = 25$ $5$ $\times$ $5$ $=$ $25$ instead of $5 \times 5 \times 5 = 125$ $5$ $\times$ $5$ $\times$ $5$ $=$ $125$ . Always remember that a cube involves multiplying the number three times.
Another frequent error occurs in prime factorization. Students may group factors incorrectly or miss out on forming complete triplets. For instance, while finding the cube root of 216, failing to group factors in sets of three can lead to the wrong answer.
Students also tend to ignore negative signs. A negative number raised to the power of 3 remains negative, which is an important concept often overlooked.
Lastly, many rely too much on guessing instead of using proper methods like estimation or factorization. Practicing structured steps ensures better results.

Shortcut Methods to Solve Cube Root Questions Faster

Time management is crucial in exams, and shortcut methods can help you solve questions quickly and accurately.

One effective shortcut is the last digit method. Each number from 1 to 9 has a unique cube ending pattern. For example, if a number ends in 7, its cube ends in 3. This helps in identifying cube roots of large numbers within seconds.

Another method is estimation using nearest perfect cubes. For instance, if you need to find the cube root of 2000, you know that:
$12^3 = 1728$ $12$ $3$ $=$ $1728$ and $13^3 = 2197$ $13$ $3$ $=$ $2197$
Since 2000 lies between these, the cube root will be between 12 and 13.

You can also use breaking numbers into parts to simplify calculations. For example:

(20)^3 = 8000

$($ $20$ $)$ $3$ $=$ $8000$

This helps in quickly solving questions involving larger values.

Using these shortcuts regularly can improve both speed and confidence during exams.

Importance of Cube and Cube Roots in Higher Classes

Understanding cubes and cube roots in Class 8 builds a strong foundation for advanced mathematical concepts in higher classes.

In Class 9 and beyond, students encounter topics like algebra, polynomials, and mensuration, where cube concepts are frequently used. For example, expanding expressions like $(a + b)^3$ $($ $a$ $+$ $b$ $)$ $3$ directly depends on understanding cubes.

Cubes are also important in geometry, especially when dealing with volumes of 3D shapes like cubes and cuboids. Without a clear understanding of cubes, solving such problems becomes difficult.

Moreover, in competitive exams and real-life applications, cube roots are used in calculations related to data, measurements, and even coding algorithms.

So, mastering this topic now not only helps in scoring well in Class 8 but also makes future maths learning smoother and more intuitive.

PlanetSpark: Make Math Learning Simple and Fun

If your child finds topics like cube and cube roots confusing, the right guidance can make all the difference. PlanetSpark’s interactive learning approach helps students understand concepts step-by-step instead of just memorizing formulas.

Live 1:1 sessions for personalized attention and better understanding
Expert teachers who simplify complex maths concepts
Engaging activities that make learning interactive and fun
Focus on building strong logical and problem-solving skills
Curriculum aligned with school learning for better academic performance
Practical teaching approach to make concepts easy to grasp
Helps in mastering NCERT topics with clarity
Supports effective exam preparation and boosts confidence

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Conclusion

The chapter Cube and Cube Roots Class 8 is one of the most scoring and concept-based topics in mathematics. Once you understand the logic behind cubes and practice regularly, solving even tricky questions becomes easy.

Start with basics, memorize key cubes, and gradually move to advanced problems. With consistent practice, you can also explore class 8 maths square and square roots so you’ll not only score well in exams but also build a strong foundation for higher-level math.

Frequently Asked Questions

A cube of a number is the result of multiplying the number by itself three times. It is represented as

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=27.