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 option is 20.

To estimate the approximate value that replaces the question mark (?), we round each number in the equation to its nearest convenient integer:

• $129.92\approx 130$

• $199.89\approx 200$

• $40.01\%\approx 40\%$

• $160.21\approx 160$

• $6.12\approx 6$

Now, substitute these approximate values back into the equation:

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

First, calculate $40\%\text{of}160$:

$40\%\text{of}160=\frac{40}{100}\times 160=4\times 16=64$

Next, add all the values on the left side together:

$130+200+64+6={?}^2$

$400={?}^2$

Finally, take the square root of both sides to find the value of ?:

$?=\sqrt{400}=20$

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