Class 8 Mathematics: Cubes and Cube Roots Mastery

How this worksheet helps your child

• Builds confidence in core Mathematics concepts taught in Class 8 through repeated, varied practice.
• Aligned to CBSE and NCERT — questions mirror the pattern children see in school tests and unit assessments.
• Comes with an answer key so parents and students can self-check in minutes, without needing a teacher.
• Pitched at hard level — use it for daily homework, weekend revision or quick exam warm-ups.

About this worksheet

Dive deep into the fascinating world of Cubes and Cube Roots with this challenging practice worksheet, designed specifically for Class 8 Mathematics students following the CBSE curriculum. This resource is perfect for students who have a foundational understanding of cubes and cube roots and are ready to tackle more complex problems. It will test your ability to identify perfect cubes, apply prime factorization methods, and solve real-world problems involving these concepts. Mastering cubes and cube roots is crucial for building a strong mathematical foundation, as these topics frequently appear in higher-level mathematics and competitive examinations. This worksheet offers a comprehensive mix of multiple-choice questions, fill-in-the-blanks, and short answer problems to ensure a thorough understanding and build confidence. Prepared with CBSE and NCERT guidelines in mind, it provides an excellent opportunity to solidify your knowledge and prepare for assessments.

What your child will learn

• Practice identifying perfect cubes through various methods.
• Apply prime factorization to find cube roots of numbers.
• Solve problems involving the properties of cubes and cube roots.
• Recognise patterns and relationships related to cubic numbers.
• Develop critical thinking skills in solving challenging mathematics problems.

Understanding the concept

Cubes and cube roots are fundamental concepts in mathematics that help us understand numbers in a different dimension. When we talk about the 'cube' of a number, we mean multiplying that number by itself three times. For example, the cube of 2 is 2 × 2 × 2, which equals 8. We often write this as 2³. A 'perfect cube' is a number that can be obtained by cubing an integer, like 8 (from 2) or 27 (from 3). The 'cube root' is the inverse operation, where we find the number that, when cubed, gives us the original number. So, the cube root of 8 is 2, because 2³ = 8. We denote the cube root using a symbol like a square root, but with a small '3' above it (³√). For example, ³√27 = 3. Understanding how to find cube roots, often using a method called prime factorization, is very important. Prime factorization involves breaking down a number into its prime factors (numbers only divisible by 1 and themselves, like 2, 3, 5). For instance, to find the cube root of 64, we factorize it as 2 × 2 × 2 × 2 × 2 × 2. Since we need groups of three identical factors for a cube root, we can group them as (2 × 2 × 2) × (2 × 2 × 2). Each group gives us one '2', so ³√64 = 2 × 2 = 4. This topic helps children understand volume calculations and abstract number properties.

Tips for parents & teachers

• Encourage your child to work through the problems independently first, then review their answers together.
• For challenging problems, guide your child to recall the properties of cubes and prime factorization steps.
• Discuss real-life examples where cubes and cube roots might be used, such as in calculating volumes.
• Use a timer to help your child practice solving problems efficiently, which is useful for exams.
• Review the solved problems to identify any common mistakes and reinforce correct methods.

Topics covered

How to use this worksheet at home

Open the print view and use your browser's Print dialog to print on regular A4 paper or save as a PDF. Hand the printed sheet to your child (Class 8) and set a relaxed time limit — 15 to 25 minutes works for most Mathematics worksheets. When they're done, open the "With answer key" view and let them self-mark question by question. Re-print as many times as you need; the file never expires and there's no download limit.

Frequently asked questions

Is this Mathematics worksheet really free?

Yes — every workbook on WorkbookWala is 100% free to download and print. No login, no email, no paywall. We're free for students, parents and teachers.

Is it aligned to the CBSE / NCERT syllabus?

Yes. All Class 8 worksheets are built around the CBSE and NCERT pattern so they map cleanly to what your child is studying in school.

Can I print this worksheet at home?

Yes. Click "Open print view" and use your browser's Print dialog to print on standard A4 paper, or save it as a PDF for later. The layout is designed to fit cleanly without scaling.

Does it include an answer key?

Yes — click "With answer key" to print a version with answers included, so parents and students can self-mark in minutes.