Perfect square means the product of two identical integers.

Eg. 5 x 5 = 5² = 25


3276 has prime factors 2², 3² , 7 and 13.

In order to have a perfect square, you need an equal number of the same type of prime factor on each side to make up each integer.

2² and 3² can be distributed equally, one 2 and one 3 for each integer.


Since 3276 has only one 7 and one 13, we need a minimum of one more 7 and one more 13 such that we can distribute one 7 and one 13 to each integer.



Minimum value of r = 13 × 7 = 91

See how it works :

When r = 91,

3276r

= 3276 × 91

= 2² × 3² × 7 × 13 × 7 × 13

= 2 × 2 × 3 × 3 × 7 × 7 × 13 × 13

(Or 2² × 3² × 7² × 13²)

= (2 × 3 × 7 × 13) × (2 × 3 × 7 × 13)

= (2 × 3 × 7 × 13)²

(or 546 × 546)

= 546 ²