Each side of a square classroom is 9 yards long. The school wants to replace the carpet in the classroom with new carpet that costs $66.00 per square yard. How much will the new carpet cost?

To find the cost of the new carpet for the square classroom, we first need to calculate the area of the classroom.

The area \(A\) of a square is given by the formula: \[ A = \text{side}^2 \] Here, the length of each side is 9 yards.

Calculating the area: \[ A = 9^2 = 81 \text{ square yards} \]

Next, we need to determine the total cost of the carpet. The cost per square yard is $66.00. Therefore, the total cost \(C\) can be calculated as follows: \[ C = \text{area} \times \text{cost per square yard} \] Substituting the known values: \[ C = 81 \text{ square yards} \times 66 \text{ dollars/square yard} \]

Now, performing the multiplication: \[ C = 81 \times 66 = 5346 \text{ dollars} \]

Thus, the total cost of the new carpet will be: \[ \boxed{5346} \text{ dollars} \]