Greatest Five Digit Square Number Calculation

To find the greatest five-digit square number, we need to identify the largest perfect square that does not exceed the largest five-digit number, which is $99999$.

Finding the Square Number

Follow these steps:

• Largest Five-Digit Number: The maximum value for a five-digit number is $99999$.
• Calculate Square Root: Determine the square root of $99999$.

  $\sqrt{99999} \approx 316.2261$

• Identify Integer Root: The largest integer whose square is less than or equal to $99999$ is the integer part of the square root, which is $316$.
• Compute the Square: Calculate the square of this integer ($316$).

  $316^2 = 316 \times 316 = 99856$

• Verification: The number $99856$ is the largest perfect square within the five-digit range. Squaring the next integer, $317$, results in $317^2 = 100489$, which is a six-digit number.

Therefore, the greatest five-digit square number is $99856$. This matches Option B.