Question

The difference between the two perfect cubes is $189$. If the cube root of the smaller of the two numbers is $3$, find the cube root of the larger number.

Answer 1

Assume the variables

Let, the bigger perfect cube is $x$.

here, the cube root of a smaller number is given $3$

so, the cube of $3$ is $27$.

The smaller perfect cube is $27$.

The difference between the two perfect cubes is $189$ means,

bigger perfect cube $-$ smaller perfect cube = $189$

$$\begin{gathered} \Rightarrow x-27=189 \\ x=189+27 \\ \mathbf{}\mathit{x}\mathbf{=}\mathbf{216} \end{gathered}$$

The bigger perfect cube is $216$.

Cube root of $216$ is $6$.

Hence, the cube root of the larger number is $\mathbf{6}$.