https://file.aiquickdraw.com/mathbot/file/1726594309720wbhndtdm.jpg

Let's solve the equations highlighted in your image one by one. I'll provide step-by-step explanations for each. We will start with the marked equations:

### (ii) \( \sqrt{x - 9} = 1 \)

1. Square both sides to eliminate the square root:
   \[
   (\sqrt{x - 9})^2 = 1^2
   \]
   \[
   x - 9 = 1
   \]

2. Add 9 to both sides to solve for \( x \):
   \[
   x = 10
   \]

### (v) \( \sqrt{\frac{3y + 12}{7}} = 3 \)

1. Square both sides to eliminate the square root:
   \[
   \left(\sqrt{\frac{3y + 12}{7}}\right)^2 = 3^2
   \]
   \[
   \frac{3y + 12}{7} = 9
   \]

2. Multiply both sides by 7:
   \[
   3y + 12 = 63
   \]

3. Subtract 12 from both sides:
   \[
   3y = 51
   \]

4. Divide by 3 to find \( y \):
   \[
   y = 17
   \]

### (viii) \( \sqrt{x - 8} = 1 \)

1. Square both sides:
   \[
   (\sqrt{x - 8})^2 = 1^2
   \]
   \[
   x - 8 = 1
   \]

2. Add 8 to both sides:
   \[
   x = 9
   \]

Would you like further details on these solutions, or should we move on to solving the remaining equations?

Here are 5 relative questions based on this topic:
1. How do you determine if a square root equation has extraneous solutions?
2. What happens when you take the square of a negative number under the square root?
3. Can square root equations have more than one solution? Why or why not?
4. How can you check if the solution to a square root equation is valid?
5. What happens if the number under the square root is negative in real-number math?

**Tip:** Always check for extraneous solutions when solving square root equations by plugging the solution back into the original equation.

Solve the following equations:
(ii) √(x - 9) = 1
(v) √((3y + 12) / 7) = 3
(viii) √(x - 8) = 1

Learn how to solve square root equations involving variables x and y. The problems include detailed step-by-step explanations of simplifying square roots and solving for the unknowns. Suitable for students in Grades 8-10.

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