Subject Experts Solutions for Chapter: Cubes and Cube Roots, Exercise 1: Worksheet 1

$4104$ and $13832$ are Hardy-Ramanujan numbers_____.

$13832=5832+8000={18}^3+{20}^3$, state the given expression is true or false.

Each prime factor appears three times in its cubes _____.

In prime factorization of any number, if each factor appears three times, then the number is not a perfect cube.

Prime factorization of $600$ is $2\times 2\times 2\times 3\times 5\times 5$, in which $3\times 5\times 5$ remains after grouping the $2\text{'}\mathrm{s}$ in triplets, so $600$ is a perfect cube_____.

Is $392$ a perfect cube? If smallest natural number by which $392$ must be multiplied to get a perfect cube.

Is $2376$ a perfect cube? If not, then by which smallest natural number should $2376$ be divided, so that the quotient is a perfect cube?

Using prime factorization, find if $128$ is a perfect cube.