Using prime factorisation, find which of the following are perfect squares.

(a) 484 (b) 11250

(c) 841 (d) 729

(a) Given: 484

Factors of 484 = 2 ×2 × 11 × 11

= 2² × 11²

As we see, 484 is a perfect square.

(b) Given: 11250

Factors of 11250 = 2 × 3 × 3 × 5× 5 × 5 × 5

= 2¹ × 3²× 5²× 5²

As we see, 2 has no pair.

So, 11250 is not a perfect square.

(c) Given: 841

Factors of 841 = 29 ×29

= 29²

As we see, 841 is a perfect square.

(d) Given: 729

Factors of 729 = 3 × 3 × 3 × 3 × 3 × 3

= 3²× 3²× 3²

So, 729 is a perfect square.