Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Further, find the cube root of the product.
First we find out the prime factors of 3600,
3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 23 × 32 × 52 × 2
∵ only one triples is formed and three factors remained ungrouped in triples.
Hence, 3600 is not a perfect cube.
To make it a perfect cube we have to multiply it by ( 2 × 2 × 3 × 5) = 60
3600 × 60 = 216000 ( which is a perfect cube of 60)