Yes, all even numbers squared are divisible by 4.
Explanation:
An even number can be represented as 2n, where n is any integer. When we square an even number, we get:
(2n)² = 4n²
Since 4n² is a multiple of 4, it is always divisible by 4. Therefore, the square of any even number is always divisible by 4.
Examples:
- 2² = 4 (4 is divisible by 4)
- 4² = 16 (16 is divisible by 4)
- 6² = 36 (36 is divisible by 4)
- 10² = 100 (100 is divisible by 4)
- 28² = 784 (784 is divisible by 4)
Why does this work?
The key is the definition of an even number and the properties of squaring. By definition, an even number has a factor of 2. When you square an even number (2n), you are essentially multiplying (2n) by itself, resulting in (2n)(2n) = 4n². The presence of the factor '4' guarantees divisibility by 4.
