Question

What is the smallest number by which 18252 must be multiplied to make it a perfect cube? Also find cube roots of perfect cube so obtained.

Answer 1

Hi there!
Here's the answer:

• The Prime Factorization of 18252 is:
18252= 2 × 2 × 3 × 3 × 3 × 13 × 13
• In Exponential Form:
18252= 2² × 3³ × 13²
(Here multiply the powers of prime factor not having 3 as their powers)

To make it a perfect cube, 18252 is to be multiplied by 26(i.e., 2×13)

The No. is 18252×26= 474552
The cube root of is 2×3×13= 338.


:)
Hope it helps