Question

Which of the following numbers are perfect squares?
11, 12, 16, 32, 36, 50, 64, 79, 81, 111, 121

Answer 1

11: The perfect squares closest to 11 are 9 (9 = 3²) and 16 (16 = 4²). Since 3 and 4 are consecutive numbers, there are no perfect squares between 9 and 16, which means that 11 is not a perfect square.
12: The perfect squares closest to 12 are 9 (9 =3²) and 16 (16 = 4²). Since 3 and 4 are consecutive numbers, there are no perfect squares between 9 and 16, which means that 12 is not a perfect square.
16 = 4²
32: The perfect squares closest to 32 are 25 (25 = 5²) and 36 (36 = 6²). Since 5 and 6 are consecutive numbers, there are no perfect squares between 25 and 36, which means that 32 is not a perfect square.
36 = 6²
50: The perfect squares closest to 50 are 49 (49 = 7²) and 64 (64 = 8²). Since 7 and 8 are consecutive numbers, there are no perfect squares between 49 and 64, which means that 50 is not a perfect square.
64 = 8²
79: The perfect squares closest to 79 are 64 (64 = 8²) and 81 (81 = 9²). Since 8 and 9 are consecutive numbers, there are no perfect squares between 64 and 81, which means that 79 is not a perfect square.
81 = 9²
111: The perfect squares closest to 111 are 100 (100 = 10²) and 121 (121 = 11²). Since 10 and 11 are consecutive numbers, there are no perfect squares between 100 and 121, which means that 111 is not a perfect square.
121 = 11²

Hence, the perfect squares are 16, 36, 64, 81 and 121.