https://file.aiquickdraw.com/mathbot/file/172814937246277daqvha.jpg

Let's analyze the problem shown in the image.

The given information is:

**(b)** If \( (x - 1, 11) = (8, y + 3) \), then \( \sqrt{x + 2y} = \ldots \)

### Step 1: Solving for \( x \) and \( y \)
Given that two ordered pairs are equal:

\[
(x - 1, 11) = (8, y + 3)
\]

This implies that:

1. \( x - 1 = 8 \)
2. \( 11 = y + 3 \)

#### Solving the equations:
1. \( x - 1 = 8 \Rightarrow x = 8 + 1 = 9 \)
2. \( 11 = y + 3 \Rightarrow y = 11 - 3 = 8 \)

So, \( x = 9 \) and \( y = 8 \).

### Step 2: Finding \( \sqrt{x + 2y} \)

Now, substitute \( x = 9 \) and \( y = 8 \) into the expression \( \sqrt{x + 2y} \):

\[
\sqrt{x + 2y} = \sqrt{9 + 2(8)} = \sqrt{9 + 16} = \sqrt{25} = 5
\]

### Final Answer
\[
\sqrt{x + 2y} = 5
\]

Let me know if you would like a detailed explanation of any step, or if you have more questions.

#### Additional Related Questions:
1. What would happen if \( x \) and \( y \) were variables instead of specific values?
2. How would the value of \( \sqrt{x + 2y} \) change if \( x \) was increased by 2?
3. How would you solve the problem if \( x \) and \( y \) were complex numbers?
4. What is the geometric interpretation of the given pair equality?
5. How would you find \( \sqrt{x + 2y} \) if it involved additional constraints?

#### Tip
Always make sure to isolate variables systematically when dealing with equal pairs to avoid confusion.

If (x - 1, 11) = (8, y + 3), then find the value of √(x + 2y).

Learn how to solve for x and y using the equality of ordered pairs, and find the square root of the resulting expression √(x + 2y). This problem covers algebraic concepts and is suitable for students in Grades 8-10.

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