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A crate is packed completely with 1 cm cubes that together form one large cube with no gaps. If 4096 small cubes are used, how many lie along one edge?

Class 8Cubes and Cube RootsCubes and Roots
  • A16
  • B14
  • C18
  • D64

Step-by-Step Solution

The count along an edge is . Since , the answer is 16. Choosing 64 takes the square root instead — that would be the number of cubes on one face, not along one edge.
Answer: A) 16

Key idea: Cube root of negative integers

Cube roots of negatives are real numbers (unlike square roots).

∛ = −∛.

Example: ∛(−125). . So ∛.

This is one place where square root and cube root behave differently — square roots of negatives are NOT real (they're imaginary, a Class 11 topic). Cube roots of negatives are perfectly normal.

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