CBSE · Class 8 · Mathematics · Cube and Cube RootsBy what smallest natural number should 81 be divided so that the quotient is a perfect cube?
Step-by-Step Solution
Prime factorization of $81 = 3 \times 3 \times 3 \times 3$. Here, one 3 is left over after forming a triplet. Dividing by 3 gives $81 \div 3 = 27$, which is a perfect cube ($3^3$). Thus, the smallest number is 3.
Detailed Options Breakdown
Option : 3 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: 9
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Cube and Cube Roots.
Option 2: 27
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Cube and Cube Roots.
Option 3: 2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Cube and Cube Roots.
💡 Study Guide: This question tests core syllabus concepts from Cube and Cube Roots. For formulas, key summaries, and mock exam reference guides, read the full Cube and Cube Roots Revision Notes.