Since,

189 = 3² × 3 × 7

It cannot be written as pair of two equal factors, so 189 is not a perfect square

Since,

225 = (5 × 5) × (3 × 3)

It can be written as pair of two equal factors, so 22 is a perfect square

Since,

2048 = (2 × 2) × (2 × 2) × (2 × 2) (2 × 2) × (2 × 2) × 2

All the factors cannot be written as pair of two equal factors, so 189 is not a perfect square

Since,

343 = (7 × 7) × 7

It cannot be written as pair of two equal factors, so 343 is not a perfect square

Since,

441 = (7 × 7) × (3 × 3)

It can be written as pair of two equal factors, so 441 is a perfect square

Since,

2916 = (3 × 3) × (3 × 3) × (3 × 3) × (2 × 2)

It can be written as pair of two equal factors, so 2916 is a perfect square

Since,

11025 = (5 × 5) × (3 × 3) × (7 × 7)

It can be written as pair of two equal factors, so 11025 is a perfect square

Since,

3549 = (13 × 13) × 3 × 7

It cannot be written as pair of two equal factors, so

3549 is not a perfect square