${?}^2\times (19.99\%\text{of}399.97+5.992^{\mathrm{}})=1856.03$

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

The correct option is 4.

We need to find the approximate value of the question mark (?) in the following given equation:

${?}^2\times (19.99\%\text{of}399.97+{5.99}^2)=1856.03$

Step 1: Round off the values to their nearest whole numbers for approximation.
- 19.99% ≈ 20%
- 399.97 ≈ 400
- 5.99 ≈ 6
- 1856.03 ≈ 1856

Let the unknown value (?) be represented by $x$.

Substituting these approximate values into the equation, we get:

$x^2\times (20\%\text{of}400+6^2)=1856$

Step 2: Calculate the terms inside the parentheses.
First, find 20% of 400:

$20\%\text{of}400=\frac{20}{100}\times 400=80$

Next, find the square of 6:

$6^2=36$

Now, add the two values inside the parentheses:

$80+36=116$

Step 3: Solve for $x^2$.
Substitute 116 back into the simplified equation:

$x^2\times 116=1856$

Divide both sides by 116:

$x^2=\frac{1856}{116}$

$x^2=16$

Step 4: Find the value of $x$.
Take the square root of both sides:

$x=\sqrt{16}=4$

Hence, the approximate value that should come in place of the question mark (?) is 4.