Question

81 - Find the smallest number by which the given number must be multiplied to obtain a perfect cube?

Answer 1

Hey there!

81 = 3 * 27

= 3 * 3³

$= {3}^{4}$


So, To make the given number a perfect cube, You need to have two more 3 as part of its prime factorization.

3 * 3 = 9

The least number by which 81 be multiplied to get a perfect cube is 9

Multiplying 81 by 9 , you obtain 729

whose prime factorization has triplets of 9

729 = 9³

Therefore, The smallest number by which the given number 81 should be multiplied to obtain a perfect cube is 9

Answer 2

HI ,

Resolving 81 into prime factors , we get

81 = 3 × 3 × 3 × 3

= ( 3 × 3 × 3 ) × 3

The Prime factor 3 does not appear

in a group of three .

So, 81 is not a perfect cube .

Hence , the smallest number by which

it is to be multiplied to make it a perfect

cube is 3 × 3 = 9

I hope this helps you.

: )