Chapter 4 · ICSE Class 8 Mathematics

Cubes and Cube-Roots

Learn to recognize perfect cubes, and find cube roots using prime factorization.

🧊 Chapter 4

Finding the cube root of 512 by grouping prime factors in threes The number 512 broken into prime factors of 2, grouped into three sets of three factors each, with one factor taken from each group to find the cube root equal to 8 512 = 2×2×2 × 2×2×2 × 2×2×2 Group factors in threes ∛512 = 2 × 2 × 2 = 8
4.1

Perfect Cubes

A perfect cube is a number that results from multiplying a whole number by itself three times. Just like perfect squares, recognizing perfect cubes helps identify numbers with whole-number cube roots.

1

Is 27 a perfect cube?

Yes, since 3 × 3 × 3 = 27

2

Is 20 a perfect cube?

No, since no whole number cubed gives 20

4.2

Finding Cube Roots by Prime Factorization

To find the cube root of a perfect cube, break it into prime factors, then group identical factors in threes — each group contributes one factor to the cube root.

1

Find the cube root of 216 using prime factorization.

216 = 2×2×2×3×3×3; grouping in threes gives ∛216 = 2×3 = 6

2

Find the cube root of 1000 using prime factorization.

1000 = 2×2×2×5×5×5; ∛1000 = 2×5 = 10

Practice

Exercises

1. Is 125 a perfect cube? If so, what is its cube root?

2. Is 40 a perfect cube?

3. Find the cube root of 343 using prime factorization.

4. Find the cube root of 512 using prime factorization.

5. Find the cube root of 2744 using prime factorization.

Next chapter — Chapter 5: Playing with Numbers 🔢 →