Question

(iii) Find the smallest whole number h such that4704/his a cube number.​

Answer 1

Answer:

$h=588$

Step-by-step explanation:

Given the fraction $\dfrac{4,704}{h}$

Consider its numerator and factor it:

$4,704=2^5\cdot 3\cdot 7^2$

You cann not take the cube root from $3, 7^2, 2^5,$ you can only take the cube root from $2^3$, then the smallest whole number $h$ such that $\dfrac{4,704}{h}$ is a cube number is

$h=2^2\cdot 3\cdot 7^2=4\cdot 3\cdot 49=588$

When $h=588,$

$\dfrac{4,704}{588}=8=2^3$