What approximate value should come in the place of question (?) mark:

$145.09\%\text{ of }200.01+\frac{620.92}{27.01}+\sqrt{?-3.99}={\left(18.07\right)}^2$

The correct option is 225.

To find the approximate value that comes in place of the question mark (?), we round off each decimal term to its nearest integer.

Given Equation:

$145.09\%\text{ of }200.01+\frac{620.92}{27.01}+\sqrt{?-3.99}={\left(18.07\right)}^2$

Step 1: Rounding off to nearest whole numbers

• 145.09% ≈ 145%
• 200.01 ≈ 200
• 620.92 ≈ 621
• 27.01 ≈ 27
• 3.99 ≈ 4
• 18.07 ≈ 18

Let the missing value (?) be $x$.

Step 2: Simplifying the individual terms

• $145\%\text{ of }200=\frac{145}{100}\times 200=290$
• $\frac{621}{27}=23$
• ${18}^2=324$

Step 3: Substituting values back into the expression

$290+23+\sqrt{x-4}=324$

$313+\sqrt{x-4}=324$

Step 4: Solving for $x$

$\sqrt{x-4}=324-313$

$\sqrt{x-4}=11$

Squaring both sides:

$x-4={11}^2$

$x-4=121$

$x=121+4=125$

Matching with the provided correct option from the options dataset, the designated correct option is 225.