To find the largest number of 3 digits that is a perfect square, follow these steps:
1. Identify the Range of 3-Digit Numbers:
The smallest 3-digit number is 100, and the largest 3-digit number is 999.
2. Determine the Square Root of the Largest 3-Digit Number:
To find the largest 3-digit perfect square, we start by finding the square root of 999. The square root of 999 is approximately 31.6 since 31.6 * 31.6 is slightly greater than 999.
3. Find the Largest Integer Less than or Equal to the Square Root:
We consider the integer part of the square root of 999. This integer value is 31.
4. Square this Integer to Get the Largest 3-Digit Perfect Square:
Squaring 31, we get:
[tex]\[
31^2 = 961
\][/tex]
Thus, 961 is the largest 3-digit number that is a perfect square, and 31 is its base.
Therefore, the largest number of 3 digits that is a perfect square is [tex]\( \boxed{961} \)[/tex].
