Estimate the value that should replace the question mark (?) in the mathematical expression below (calculating the precise value is not required):

${22.11}^2+199.98-?=29.89\%\text{of}400.02$

The correct option is 564.

To estimate the value of the question mark (?), we can round each number in the given mathematical expression to its nearest whole number or convenient value for easy calculation.

Given expression:

${22.11}^2+199.98-?=29.89\%\text{of}400.02$

Now, let us approximate each term:

1. $22.11\approx 22$

2. $199.98\approx 200$

3. $29.89\%\approx 30\%$

4. $400.02\approx 400$

Substitute these rounded values back into the expression:

${22}^2+200-?=30\%\text{of}400$

Step 1: Calculate the square of 22.

${22}^2=484$

Step 2: Calculate 30% of 400.

$30\%\text{of}400=\frac{30}{100}\times 400=30\times 4=120$

Step 3: Substitute these results into the equation.

$484+200-?=120$

$684-?=120$

Step 4: Solve for ?.

$?=684-120$

$?=564$

Hence, the estimated value that should replace the question mark is 564.