Choose the correct answer for the following:
Find the smallest number by which the number 108 must be multiplied to obtain a perfect cube
Prime Factorization:
⇒ 108 = 2 × 2 × 3 × 3 × 3
In the above Factorization, 2 × 2 remains after grouping the 3’s in triplets.
∴ 108 is not a perfect cube.
To make it a perfect cube, we multiply it by 2.
Prime Factorization:
⇒ 108 × 2 = 2 × 2 × 2 × 3 × 3 × 3
⇒ 216 = 23 × 33
= (2 × 3)3
= 63 which is a perfect cube.
∴ The smallest number by which the number 108 must be multiplied to obtain a perfect cube is 2.
AI is thinking…
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.