Theory:

1. Find the cube of \(21\).
 
Solution:
 
If you multiply a number by itself and then by itself again (thrice), the result is a cube number.
 
\(21 = 21 \times 21 \times 21 = 9261\)
 
Therefore, the cube of \(21\) is \(9261\).
 
 
2. Is \(625\) is a perfect cube? If not, make it as a perfect cube by the multiplication of smallest number.
 
Solution:
 
5|625¯5|125¯5|25¯5|5¯|1
 
Group the factors in pair of three numbers.
 
\(125 = (5 \times 5 \times 5) \times 5\)
 
Here, factor \(5\) is leftover.
 
So, \(625\) is not a perfect cube.
 
To make it as a perfect cube, we need two more \(5\)'s.
 
So, multiply the given number by two \(5\)'s.
 
\(625 \times 5 \times 5 = 15625\)
 
Therefore, \(15625\) is a perfect cube.
 
 
3. Is \(243\) is a perfect cube? If not, find the smallest number to divide \(243\) to make it as a perfect cube.
 
Solution:
 
\(243 = (3 \times 3 \times 3) \times 3 \times 3\)
 
Here, factor \(3 \times 3 = 9\) is leftover while grouping.
 
So, \(243\) is not a perfect cube.
 
To make it as a perfect cube, divide the given number by the leftover factor \(9\).
 
2439=27
 
Therefore, \(9\) is the smallest number to divide \(243\), and the obtained perfect square is \(27\).