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Important Questions

Cubes and Cube Roots

ICSE · Class 8 · Mathematics

Most important questions from Cubes and Cube Roots for ICSE Class 8 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

40 questions25 flashcards5 concepts

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40 Questions·
multiple choice

Sample Questions

1multiple choice
1 marks

What is the least number by which 1029 must be divided so that the quotient is a perfect cube?

Show answer

3

Step 1: Find prime factors of 1029. Step 2: 1029 ÷ 3 = 343; 343 = 7 × 7 × 7. Step 3: So 1029 = 3 × 7 × 7 × 7 = 3 × (7×7×7). Step 4: The triplet of 7 is complete, but 3 appears only once (incomplete triplet). Step 5: Divide by 3 → 1029 ÷ 3 = 343 = 7³, which is a perfect cube. The answer is 3.

2multiple choice
1 marks

Find the cube root of 0.216.

Show answer

0.6

Step 1: Convert 0.216 to a fraction: 0.216 = 216/1000. Step 2: Find cube root of numerator: ∛216 = ∛(6×6×6) = 6. Step 3: Find cube root of denominator: ∛1000 = ∛(10×10×10) = 10. Step 4: So ∛(216/1000) = 6/10 = 0.6. Step 5: Verify: 0.6³ = 0.6×0.6×0.6 = 0.216. ✓ A common mistake is to forget to convert to a fraction first.

3multiple choice
1 marks

What is the cube of -9?

Show answer

-729

Step 1: We need (-9)³ = (-9) × (-9) × (-9). Step 2: (-9) × (-9) = +81 (negative × negative = positive). Step 3: 81 × (-9) = -729 (positive × negative = negative). Step 4: So (-9)³ = -729. Remember: the cube of a negative number is always negative because you multiply negative sign an odd number (3) of times. A common mistake is to write +729 by forgetting the sign.

4multiple choice
1 marks

What is ∛(-512)?

Show answer

-8

Step 1: ∛(-512) = -(∛512), since cube root of a negative number is negative. Step 2: Find ∛512: prime factorise 512 = 2⁹ = (2×2×2) × (2×2×2) × (2×2×2). Step 3: ∛512 = 2 × 2 × 2 = 8. Step 4: Therefore ∛(-512) = -8. Step 5: Verify: (-8)³ = (-8)×(-8)×(-8) = 64×(-8) = -512. ✓

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Frequently Asked Questions

What are the important topics in Cubes and Cube Roots for ICSE Class 8 Mathematics?
Key topics in Cubes and Cube Roots include Flowchart showing how cubing a negative number results in a negative answer through step-by-step multiplication, Distribution showing that most numbers are not perfect cubes, Decision flowchart for identifying perfect cubes using prime factorization. These are the concepts ICSE Class 8 examiners draw on most — study them first, then practise related questions.
How to score full marks in Cubes and Cube Roots — ICSE Class 8 Mathematics?
Understand the core concepts first, then work through the 40 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Cubes and Cube Roots?
There are 40 practice questions available for Cubes and Cube Roots. These cover multiple question types including MCQs, short answer, and long answer questions.

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