- A64
- B8
- C88
- D176
Step-by-Step Solution
is already a perfect cube, and the lone 11 can never form a triple, so divide it out: . Answering 8 gives the cube root of the quotient rather than the quotient the question asks for.
Answer: A) 64
Meena divides 704 by the smallest whole number that leaves a perfect cube. Given , what quotient does she get?
Class 8Cubes and Cube RootsCubes and Roots
Key idea: Cube root by prime factorisation
**Step 1**: factorise into primes.
**Step 2**: group the prime factors into TRIPLES (three of the same).
**Step 3**: take ONE factor from each triple — their product is the cube root.
Example: ∛216. . So ∛216 = 6.
Example: ∛13824. . So ∛13824 = 24.
If any prime doesn't form a complete triple, the number isn't a perfect cube.
**Step 2**: group the prime factors into TRIPLES (three of the same).
**Step 3**: take ONE factor from each triple — their product is the cube root.
Example: ∛216. . So ∛216 = 6.
Example: ∛13824. . So ∛13824 = 24.
If any prime doesn't form a complete triple, the number isn't a perfect cube.
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