(iii) 72 = 2 × 2 × 2 × 3 × 3
The prime factor 3 does not appear in a group of three.
Therefore, 72 is not a perfect cube.
To make it a cube, we need one more 3.
In that case,
72 × 3 = 2 × 2 × 2 × 3 × 3 × 3 = 216, which is a perfect cube.
Hence, the required smallest number by which 72 should be multiplied to
make a perfect cube is 3.
(iv) 675 = 3 × 3 × 3 × 5 × 5
The prime factor 5 does not appear in a group of three.
Therefore, 675 is not a perfect cube.
To make it a cube, we need one more 5.
In that case,
675 × 5 = 3 × 3 × 3 × 5 × 5 × 5 = 3375, which is a perfect cube.
Hence, the required smallest number by which 675 should be multiplied to
make a perfect cube is 5.
(v) 100 = 2 × 2 × 5 × 5
The prime factors 2 and 5 do not appear in a group of three.
Therefore, 100 is not a perfect cube.
To make it a cube, we need one more 2 and 5respectively.
In that case,
100 × 10 = 2 × 2 × 2 × 5 × 5 × 5 = 1000, which is a perfec cube.
Hence, the required smallest number by which 100 should be multiplied to
make a perfect cube is (2 × 5), i.e, 10.