Question Mark Value Calculation

This explanation details how to determine the value needed to replace the question mark (?) in the mathematical expression provided.

The expression given is:

$$ \sqrt{196} - 114 + 96 + 112 - 187 = ? $$

Square Root Calculation

The initial step involves calculating the square root of 196.

$$ \sqrt{196} = 14 $$

This is correct because $14 \times 14 = 196$.

Substituting the Square Root

Next, substitute the calculated square root value (14) back into the original expression:

$$ 14 - 114 + 96 + 112 - 187 = ? $$

Performing Arithmetic Operations

Now, perform the addition and subtraction operations in order from left to right:

• First, calculate $14 - 114$:

  $$ 14 - 114 = -100 $$

• Then, add 96 to the current result: $-100 + 96$

  $$ -100 + 96 = -4 $$

• Add 112 to the result: $-4 + 112$

  $$ -4 + 112 = 108 $$

• Finally, subtract 187 from the result: $108 - 187$

  $$ 108 - 187 = -79 $$

Following these steps, the value of the expression is found to be -79.

Final Result Comparison

The computed value is -79. Comparing this result against the provided multiple-choice options:

• Option 1: -79
• Option 2: 79
• Option 3: -89
• Option 4: 89
• Option 5: None of these

The calculated value, -79, matches Option 1.