- A512
- B625
- C800
- D1024
Step-by-Step Solution
, so it is a perfect cube. For and the prime exponents are not multiples of 3, so neither is a cube — 625 tempts because it is a perfect square fails on both primes.
Answer: A) 512
Sonia writes down four numbers: 512, 625, 800 and 1024. Exactly one of them is a perfect cube. Which one?
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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