We need to solve the equation:

\[
\sqrt{x - 3} + 5 = 15
\]

### Step 1: Isolate the square root term
First, subtract 5 from both sides:

\[
\sqrt{x - 3} = 15 - 5
\]
\[
\sqrt{x - 3} = 10
\]

### Step 2: Square both sides
Now, square both sides to eliminate the square root:

\[
(\sqrt{x - 3})^2 = 10^2
\]
\[
x - 3 = 100
\]

### Step 3: Solve for \( x \)
Now, add 3 to both sides to isolate \( x \):

\[
x = 100 + 3
\]
\[
x = 103
\]

### Final Answer:
\[
x = 103
\]

Would you like any further details or have any questions?

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Here are 5 questions to deepen understanding:
1. How would the solution change if the original equation was \( \sqrt{x - 3} + 5 = 12 \)?
2. What happens if the radicand (inside the square root) is negative?
3. How do you solve an equation with a square root on both sides?
4. Can square root functions have negative outputs?
5. How do you check if a solution is valid in radical equations?

**Tip:** Always check for extraneous solutions when solving equations involving square roots!

Learn how to solve the radical equation \sqrt{x - 3} + 5 = 15 with a detailed step-by-step solution. This problem covers key algebraic concepts, including isolating square roots, squaring both sides, and solving for x. Suitable for students in Grades 9-10.

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