7.1 Introduction-Cubes > No. 3(ii)

To find the smallest number by which the given number may be divided to obtain a perfect cube.

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Explanation:

Cube root

In mathematics, a cube root of a number, denoted $Description: \sqrt[3]{x}$ or x^1/3, is a number a such that a³ = x. (Our solved example in mathguru.com uses this concept)

All real numbers have exactly one real cube root and a pair of complex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8 is 2, because 2³ = 8.

http://en.wikipedia.org/wiki/Cube_root

Prime factor

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization.

To shorten prime factorization, numbers are often expressed in powers, so

$Description: 288 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 = 2^5 \times 3^2.$

(Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Prime_factor

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