Find the smallest number which when multiplied with 3600 will make t

1.	Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Further, find the cube root of the product.
Answer» Here , 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 2³ × 3² × 5² × 2 Since only one triples is formed and three factors remained ungrouped in triples. Hence ,the given number 3600 is not a perfect cube. So make it a perfect cube we have to multiply it by, (2 × 2 × 3 × 5) = 60 3600 × 60 = 216000 Cube root of 216000 is ∛216000 = ∛(60×60×60) = ∛(60³) = 60 ∴ the smallest number which when multiplied with 3600 will make the product a perfect cube is 60 and the cube root of the product is 60.

Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Further, find the cube root of the product.

Answer»

Here , 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

= 2³ × 3² × 5² × 2

Since only one triples is formed and three factors remained ungrouped in triples.

Hence ,the given number 3600 is not a perfect cube.

So make it a perfect cube we have to multiply it by,

(2 × 2 × 3 × 5) = 60

3600 × 60 = 216000

Cube root of 216000 is

∛216000 = ∛(60×60×60)

= ∛(60³)

= 60

∴ the smallest number which when multiplied with 3600 will make the product a perfect cube is 60 and the cube root of the product is 60.