https://file.aiquickdraw.com/mathbot/file/1725661175867b4hxvskp.jpg

The problem shown in your image asks to solve the equation:

\[
\sqrt{2p + 5} = \sqrt{3p + 4}
\]

and identify any extraneous solutions.

### Step 1: Square both sides to eliminate the square roots.

Squaring both sides:

\[
(\sqrt{2p + 5})^2 = (\sqrt{3p + 4})^2
\]

This simplifies to:

\[
2p + 5 = 3p + 4
\]

### Step 2: Solve for \( p \).

Now, subtract \( 2p \) from both sides:

\[
5 = p + 4
\]

Subtract 4 from both sides:

\[
p = 1
\]

### Step 3: Check for extraneous solutions.

We substitute \( p = 1 \) back into the original equation to verify if it’s valid:

\[
\sqrt{2(1) + 5} = \sqrt{3(1) + 4}
\]
\[
\sqrt{2 + 5} = \sqrt{3 + 4}
\]
\[
\sqrt{7} = \sqrt{7}
\]

Since both sides are equal, \( p = 1 \) is a valid solution.

### Conclusion:
- The solution is \( p = 1 \).
- There are no extraneous solutions in this case.

Would you like any more details, or do you have any questions?

Here are 5 related questions for further practice:
1. Solve \( \sqrt{x + 6} = \sqrt{2x + 1} \).
2. Solve \( \sqrt{3x - 1} = 2 \).
3. What are extraneous solutions, and why do they occur when solving equations with square roots?
4. Solve \( \sqrt{x + 2} + 1 = 4 \).
5. What happens when both sides of a radical equation are squared incorrectly?

**Tip:** Always check for extraneous solutions by substituting back into the original equation after solving.

Solve and identify extraneous solutions for the equation \( \sqrt{2p + 5} = \sqrt{3p + 4} \).

Learn how to solve the radical equation \( \sqrt{2p + 5} = \sqrt{3p + 4} \) and identify any extraneous solutions. This problem covers key algebraic concepts, including squaring both sides and verifying solutions. Suitable for students in Grades 9-11.

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