Solving the Math Puzzle: Finding the Value of '?'

This question requires us to find the value of the unknown number represented by a question mark ('?') in a mathematical equation. We need to use the order of operations (often remembered by the acronym BODMAS/PEMDAS) to solve it correctly.

The given equation is:

$ \sqrt{?} + 40 \div 10 \times 7 - 3 = 50 $

Applying the Order of Operations (BODMAS/PEMDAS)

The BODMAS rule stands for Bracket, Order (powers and square roots), Division, Multiplication, Addition, and Subtraction. We solve the operations in this specific sequence.

1. Division: First, perform the division.

   $ 40 \div 10 = 4 $

   The equation now looks like: $ \sqrt{?} + 4 \times 7 - 3 = 50 $

2. Multiplication: Next, perform the multiplication.

   $ 4 \times 7 = 28 $

   The equation simplifies to: $ \sqrt{?} + 28 - 3 = 50 $

3. Addition/Subtraction: Now, perform addition and subtraction from left to right. First, subtract 3 from 28.

   $ 28 - 3 = 25 $

   The equation becomes: $ \sqrt{?} + 25 = 50 $

4. Isolate the Square Root: To find the value under the square root, we need to isolate it on one side of the equation. Subtract 25 from both sides.

   $ \sqrt{?} = 50 - 25 $

   $ \sqrt{?} = 25 $

5. Find the Square Root Value: The final step is to find the number whose square root is 25. We do this by squaring both sides of the equation.

   $ (\sqrt{?})^2 = 25^2 $

   $ ? = 625 $

Conclusion

By following the order of operations step-by-step, we find that the value of '?' in the equation is 625.