(i) Can a rectangular number be a square number?

(ii) Can a triangular number be a square number?

(i) Yes, a rectangular number can be a square number.

Reason: Yes, a rectangular number can be a square number if it can also be arranged in a square pattern.
For example, 36 can be arranged as 6 × 6, so it is a square number. It can also be arranged as 4 × 9 or 3 × 12, so it is also a rectangular number.

(ii) Yes, a triangular number can be a square number.

Reason: Some numbers are both triangular and square. For example, 1 is both the 1^st triangular number and the 1^st square number. Similarly, 36 is both a triangular number (8^th triangular number = $\dfrac{8 \times 9}{2}$ = 36) and a square number (6² = 36).