Which of these numbers 6400, 125, 9261 and 4913 is not a perfect cube?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6400
A perfect cube is a number that is some whole number multiplied by itself three times. Each number is tested by finding that whole number, or by its prime factors:
Option (1) 6400 — \(6400=2^8\times5^2\); the powers 8 and 2 are not multiples of 3, so 6400 is not a cube (it lies between \(18^3=5832\) and \(19^3=6859\)).
Option (2) 125 — \(5^3\), a perfect cube.
Option (3) 9261 — \(21^3=21\times21\times21=9261\), a perfect cube.
Option (4) 4913 — \(17^3=17\times17\times17=4913\), a perfect cube.