The problem asks us to fill in a 2x2 table with numbers less than 100. The rows are "a square number" and "not a square number," and the columns are "even" and "not even." This means we need to find a number less than 100 that fits each of the four descriptions: (1) a square number that is even, (2) a square number that is not even, (3) not a square number that is even, and (4) not a square number that is not even.

1. Problem Description

The problem asks us to fill in a 2x2 table with numbers less than

1

0

0. The rows are "a square number" and "not a square number," and the columns are "even" and "not even." This means we need to find a number less than 100 that fits each of the four descriptions: (1) a square number that is even, (2) a square number that is not even, (3) not a square number that is even, and (4) not a square number that is not even.

2. Solution Steps

First, let's identify square numbers less than

1

0

0. A square number is an integer that is the square of an integer.

$1^2 = 1$

$2^2 = 4$

$3^2 = 9$

$4^2 = 16$

$5^2 = 25$

$6^2 = 36$

$7^2 = 49$

$8^2 = 64$

$9^2 = 81$

$10^2 = 100$. We don't include this since the question asks for numbers less than

1

0

0. The square numbers less than 100 are 1, 4, 9, 16, 25, 36, 49, 64, and

8

1.

Now let's find an even square number. From the list above, the even square numbers are 4, 16, 36, and

6

4. We can pick any of these. Let's pick

4.

Next, let's find a square number that is not even (odd). From the list above, the odd square numbers are 1, 9, 25, 49, and

8

1. Let's pick

9.

Now, we need a number less than 100 that is not a square number and is even. Let's pick

6.

Finally, we need a number less than 100 that is not a square number and is not even (odd). Let's pick

7.

3. Final Answer

| | Even | Not Even |

|-------------|------|----------|

| Square Number | 4 | 9 |

| Not Square Number | 6 | 7 |