Identifying Perfect Squares Using Number Properties

To determine if a number is a perfect square, we can use two main methods: checking the last digit and calculating the square root.

Last Digit Rule Analysis

Perfect squares have specific last digits. A perfect square cannot end in 2, 3, 7, or 8.

Let's examine the last digit of each option:

• 48841 ends in 1 (Possible perfect square)
• 58287 ends in 7 (Cannot be a perfect square)
• 68763 ends in 3 (Cannot be a perfect square)
• 38262 ends in 2 (Cannot be a perfect square)

Only 48841 passes this initial check.

Square Root Verification

Now, we verify if 48841 is indeed a perfect square by calculating its square root.

Estimate the square root:

• We know that $200^2 = 40000$ and $250^2 = 62500$. Therefore, the square root of 48841 lies between 200 and 250.
• Since 48841 ends in 1, its square root must end in 1 or 9.

Let's test the number 221:

Using LaTeX for calculation:

$ 221^2 = 221 \times 221 $

$ 221 \times 221 = 48841 $

The calculation confirms that $221^2$ equals 48841.

Final Answer

The number 48841 is a perfect square because its square root is an integer (221).