Question

find the smallest number that must be multiplied to 6561 to make it a perfect cube​

Answer 1

$\huge\underbrace\red{Answer}$

Performing prime factorization of 6561,

we get

6561=3×3×3×3×3×3×3×3

6561=(3×3×3)×(3×3×3)×3×3

After grouping of the equal factors in 3’s, it’s seen that 3×3 is left ungrouped in 3’s.

In order to complete it in triplet, we should multiply it by 3.

Hence, required smallest number =3

and cube root of the product =3×3×3=27

Answer 2

Step-by-step explanation:

Performing prime factorization of 6561,

we get

6561=3×3×3×3×3×3×3×3

6561=(3×3×3)×(3×3×3)×3×3

After grouping of the equal factors in 3’s, it’s seen that 3×3 is left ungrouped in 3’s.

In order to complete it in triplet, we should multiply it by 3.

Hence, required smallest number =3

and cube root of the product =3×3×3=27