Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.
72
72
Prime Factorization:
⇒ 72 = 2 × 2 × 2 × 3 × 3
= 23 × 32
There are only two 3’s.
∴ 72 is not a perfect cube.
To make it a perfect cube, we have to multiply with 3.
⇒ 72 × 3 = 2 × 2 × 2 × 3 × 3 × 3
⇒ 216 = 23 × 33
= 63 which is a perfect cube.
∴ The smallest number by which 72 must be multiplied to obtain a perfect cube is 3.
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