Identifying Numbers That Are Not Perfect Squares

To determine which number is not a square of any natural number, we can examine the properties of perfect squares. One useful property involves the last digit of a number.

A natural number is a perfect square if and only if its last digit is one of the following: 0, 1, 4, 5, 6, or 9. Conversely, a number ending in 2, 3, 7, or 8 cannot be a perfect square.

Let's check the last digit of each given option:

• 18225 ends in 5. A number ending in 5 can be a perfect square (e.g., \(15^2 = 225\)).
• 53361 ends in 1. A number ending in 1 can be a perfect square (e.g., \(11^2 = 121\)).
• 63592 ends in 2. A number ending in 2 cannot be a perfect square.
• 17956 ends in 6. A number ending in 6 can be a perfect square (e.g., \(16^2 = 256\)).

Based on the property of the last digit, the number 63592 ends in 2, which is not possible for a perfect square of a natural number.

For confirmation, let's see if the other numbers are indeed perfect squares:

• The square root of 18225 is 135. \((135^2 = 18225)\)
• The square root of 53361 is 231. \((231^2 = 53361)\)
• The square root of 17956 is 134. \((134^2 = 17956)\)

Thus, 18225, 53361, and 17956 are perfect squares, while 63592 is not.