https://file.aiquickdraw.com/mathbot/file/1730514086699d2lkxjw8.jpg

The equation to solve is:

\[
3 = \frac{\sqrt{a + 1}}{2}
\]

### Step-by-Step Solution:

1. **Isolate the Square Root**: 
   Multiply both sides by 2 to eliminate the fraction:
   \[
   3 \times 2 = \sqrt{a + 1}
   \]
   \[
   6 = \sqrt{a + 1}
   \]

2. **Square Both Sides**: 
   To remove the square root, square both sides of the equation:
   \[
   6^2 = (\sqrt{a + 1})^2
   \]
   \[
   36 = a + 1
   \]

3. **Solve for \(a\)**: 
   Subtract 1 from both sides:
   \[
   a = 36 - 1
   \]
   \[
   a = 35
   \]

### Check for Extraneous Solutions

Substitute \( a = 35 \) back into the original equation to verify:

\[
3 = \frac{\sqrt{35 + 1}}{2}
\]
\[
3 = \frac{\sqrt{36}}{2}
\]
\[
3 = \frac{6}{2}
\]
\[
3 = 3
\]

The left side equals the right side, so \( a = 35 \) is indeed a valid solution, and there are no extraneous solutions.

### Final Answer:
\[
a = 35
\]

Would you like more details, or have any questions?

---

Here are some related questions for further practice:

1. Solve for \( x \) in \( 4 = \frac{\sqrt{x + 3}}{3} \).
2. Solve the equation \( 5 = \frac{\sqrt{2a + 4}}{3} \).
3. Solve \( 7 = \frac{\sqrt{b + 9}}{4} \).
4. Solve \( 2 = \frac{\sqrt{c + 5}}{5} \).
5. Solve \( 10 = \frac{\sqrt{d + 6}}{3} \).

**Tip:** Always check for extraneous solutions when dealing with square root equations, as squaring can introduce solutions that don’t satisfy the original equation.

Solve the equation 3 = (√(a + 1)) / 2. Check for extraneous solutions.

Learn how to solve the radical equation 3 = (√(a + 1)) / 2 step-by-step. This solution covers isolating the square root, squaring both sides, and checking for extraneous solutions, suitable for high school students in Grades 9-11.

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