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The problem states:

- \( y \) is directly proportional to the square root of \( (x + 2) \).
- When \( x = 7 \), \( y = 2 \).
- You are asked to find \( y \) when \( x = 98 \).

### Step-by-step solution:

1. **Set up the relationship**:
   Since \( y \) is directly proportional to \( \sqrt{x + 2} \), we can express this relationship as:
   \[
   y = k \sqrt{x + 2}
   \]
   where \( k \) is the constant of proportionality.

2. **Find the constant \( k \)**:
   We are given that \( y = 2 \) when \( x = 7 \). Substitute these values into the equation:
   \[
   2 = k \sqrt{7 + 2}
   \]
   \[
   2 = k \sqrt{9}
   \]
   \[
   2 = k \times 3
   \]
   Solving for \( k \):
   \[
   k = \frac{2}{3}
   \]

3. **Find \( y \) when \( x = 98 \)**:
   Now use the value of \( k = \frac{2}{3} \) to find \( y \) when \( x = 98 \):
   \[
   y = \frac{2}{3} \sqrt{98 + 2}
   \]
   \[
   y = \frac{2}{3} \sqrt{100}
   \]
   \[
   y = \frac{2}{3} \times 10
   \]
   \[
   y = \frac{20}{3}
   \]
   \[
   y \approx 6.67
   \]

### Final Answer:
When \( x = 98 \), \( y \approx 6.67 \).

Would you like more details on any step or have other questions?

Here are some related questions for further practice:

1. What happens to \( y \) if \( x \) is doubled in this type of problem?
2. How would the relationship change if \( y \) were inversely proportional to \( \sqrt{x+2} \)?
3. Can you find the value of \( y \) if \( x = 50 \) using the same method?
4. How would the result change if \( y \) was directly proportional to \( x \) instead of \( \sqrt{x + 2} \)?
5. What happens if the constant \( k \) were larger or smaller in this equation?

**Tip**: Always check if the proportionality constant \( k \) makes sense by substituting back into the original equation.

y is directly proportional to the square root of (x + 2). When x = 7, y = 2. Find y when x = 98.

Solve the direct proportionality problem where y is proportional to the square root of (x + 2). Learn how to find y when x = 98 using a step-by-step method. Suitable for students in Grades 9-11.

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