Statement 1: 3675 is not a perfect square.

Statement 2: After grouping into pairs of equal factors of 3675, if we multiply or divide by the unpaired factor (if any) then the product or the quotient becomes a perfect square.

Which of the following options is correct ?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Finding prime factors of 3675, we get :

⇒ 3675 = 3 x (5 x 5) x (7 x 7)

Since the prime factor 3 is not in pair.

∴ 3675 is not a perfect square.

So, statement 1 is true.

⇒ 3675 = 3 x (5 x 5) x (7 x 7)

Multiplying by 3 on both sides, we get :

⇒ 3675 × 3 = (3 x 3) x (5 x 5) x (7 x 7)

⇒ 11025 = (3 x 3) x (5 x 5) x (7 x 7)

Since all prime factor are in pair. Therefore, 3675 x 3 is a perfect square.

⇒ 3675 = 3 x (5 x 5) x (7 x 7)

Dividing by 3 on both sides, we get :

⇒ $\dfrac{3675}{3}$ = (5 x 5) x (7 x 7)

⇒ 1225 = (5 x 5) x (7 x 7)

Since all prime factor are in pair. Therefore, 3675 ÷ 3 is a perfect square.

So, statement 2 is true.

Hence, option 1 is the correct option.