Estimate the approximate value that should replace the question mark (?) in the following equation. (Note: You are not expected to calculate the exact value.)

$129.92+199.89+40.01\%\text{of}160.21+6.12=?{}^2$

The correct answer is 20.

To estimate the approximate value that should replace the question mark (?), we can round off each decimal number in the given equation to its nearest whole number for easier calculations.

Let us round off each component of the expression:

129.92 ≈ 130

199.89 ≈ 200

40.01% ≈ 40%

160.21 ≈ 160

6.12 ≈ 6

Now, rewrite the equation using these approximate values:

$130+200+(40\%\text{of}160)+6\approx ?{}^2$

Step 1: Calculate the percentage part.

$40\%\text{of}160=\frac{40}{100}\times 160=64$

Step 2: Add all the numbers on the left-hand side.

$130+200+64+6=400$

Step 3: Solve for ?.

$?{}^2\approx 400$

$?\approx \sqrt{400}$

$?=20$

Hence, the approximate value that should replace the question mark (?) is 20.