To solve the equation \(\sqrt{x} + 1 = 4\):

1. Subtract 1 from both sides of the equation:
   \[
   \sqrt{x} = 4 - 1
   \]
   \[
   \sqrt{x} = 3
   \]

2. Square both sides to eliminate the square root:
   \[
   x = 3^2
   \]
   \[
   x = 9
   \]

So, the solution is \(x = 9\).

Would you like more details or have any questions? Here are five related questions you might find interesting:

1. What if the equation was \(\sqrt{x} + 2 = 7\)? How would the solution change?
2. How do you solve the equation \(\sqrt{x + 3} = 5\)?
3. What are the steps to solve \(\sqrt{2x} = 8\)?
4. How would the solution change if the equation were \(\sqrt{x} - 1 = 4\)?
5. What are the possible values of \(x\) if the equation were \(\sqrt{x} + 1 = -2\)?

**Tip:** When solving square root equations, always remember to check for extraneous solutions, as squaring both sides can sometimes introduce invalid solutions.

Learn how to solve the equation sqrt(x) + 1 = 4 with a detailed step-by-step solution. This problem covers key mathematical concepts involving square roots and equations. Suitable for students in Grades 9-12.

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