$\sqrt{965}+30\%\text{ of }698+16={?}^2$
What approximate value should come in place of the question mark (?) in the following questions?

The correct answer is 16.

To find the approximate value that should come in place of the question mark (?), we simplify each term of the given equation step-by-step:

Step 1: Approximate the square root term
The number 965 is very close to 961, which is a perfect square (${31}^2=961$).
Thus, we can write:
$\sqrt{965}\approx \sqrt{961}=31$

Step 2: Approximate the percentage term
We can round 698 to 700 to simplify the calculation:
$30\%\text{ of }698\approx 30\%\text{ of }700$
Calculating the value:
$30\%\text{ of }700=\frac{30}{100}\times 700=210$

Step 3: Combine all terms in the equation
Substitute the approximated values back into the expression:
$31+210+16={?}^2$
Adding the numbers together:
$257={?}^2$

Step 4: Solve for ?
To find ?, take the square root of both sides:
$?=\sqrt{257}$
Since ${16}^2=256$, which is extremely close to 257, we get:
$?\approx 16$

Therefore, the approximate value in place of the question mark is 16.