Three square numbers greater than 100 are 121, 144, and 169. These numbers are easily identifiable as perfect squares, meaning they are the product of an integer multiplied by itself.
A square number, also known as a perfect square, is an integer that is the result of multiplying an integer by itself. For example, 121 is a square number because it is 11 multiplied by 11 (11 × 11 = 121).
Understanding Square Numbers Above 100
Exploring square numbers reveals that many fall within the three-digit range. Specifically, there are 22 square numbers that are three digits long. These numbers start from 100 (10 × 10) and extend up to 961 (31 × 31). Once a number exceeds 961, the next square number, 1024 (32 × 32), transitions into four-digit territory.The sequence of square numbers greater than 100 within the three-digit range includes:
- 121 (11 × 11)
- 144 (12 × 12)
- 169 (13 × 13)
- 196 (14 × 14)
- 225 (15 × 15)
- And many others, such as 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961.
A Glimpse at Square Numbers (Greater Than 100)
Here are some examples of square numbers greater than 100, showing their corresponding roots:| Square Number | Root (n) | Calculation (n × n) |
|---|---|---|
| 121 | 11 | 11 × 11 |
| 144 | 12 | 12 × 12 |
| 169 | 13 | 13 × 13 |
| 196 | 14 | 14 × 14 |
| 225 | 15 | 15 × 15 |
| 256 | 16 | 16 × 16 |
Key Characteristics of Square Numbers
Understanding the fundamental properties of square numbers can make them easier to identify:- Non-negative: Square numbers are always non-negative integers.
- Prime Factors: The prime factors of a perfect square always occur in pairs. For instance, the prime factors of 36 (6 × 6) are 2, 2, 3, 3.
- Unit Digits: A square number's unit digit (the last digit) can only be 0, 1, 4, 5, 6, or 9. Numbers ending in 2, 3, 7, or 8 can never be perfect squares.
