Solving the Equation Step-by-Step

This solution will guide you through finding the missing value represented by the question mark (?) in the given mathematical equation. We will break down the calculation process step-by-step to ensure clarity.

Evaluating the Expression

The equation provided is:

$$ (22 \times 15 - 150) - 164 = \sqrt{?} $$

First, we need to solve the expression on the left side of the equals sign. Let's evaluate the part inside the parentheses:

• Step 1: Multiplication

  Calculate the product of 22 and 15:

  $$ 22 \times 15 = 330 $$
• Step 2: Subtraction within Parentheses

  Subtract 150 from the result of the multiplication:

  $$ 330 - 150 = 180 $$
• Step 3: Final Subtraction

  Now, subtract 164 from the result obtained in Step 2:

  $$ 180 - 164 = 16 $$

Finding the Missing Value

After evaluating the left side of the equation, we found it equals 16. So, the equation now simplifies to:

$$ 16 = \sqrt{?} $$

To find the value of '?', we need to determine what number has 16 as its square root. This means we need to square the number 16:

• Step 4: Squaring the Result

  Square the value 16 to find the value of '?':

  $$ ? = 16^2 $$

  Calculating 16 squared:

  $$ 16 \times 16 = 256 $$

Therefore, the value that replaces the question mark (?) in the equation is 256.