Let's solve the equation \( \sqrt{100x} - 1 = 9 \).

### Step 1: Isolate the square root
First, add 1 to both sides of the equation:

\[
\sqrt{100x} = 9 + 1
\]

\[
\sqrt{100x} = 10
\]

### Step 2: Eliminate the square root
To eliminate the square root, square both sides of the equation:

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

\[
100x = 100
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 100:

\[
x = \frac{100}{100} = 1
\]

### Final Answer:
\[
x = 1
\]

Would you like more details on any of the steps or have further questions?

Here are five related questions you could explore:
1. What happens if the equation were \( \sqrt{100x} - 1 = 8 \)?
2. How would the solution change if the square root was \( \sqrt{100x + 1} \)?
3. Can you solve \( \sqrt{25x} + 3 = 8 \)?
4. What is the solution to \( \sqrt{4x} = 2 \)?
5. How would you solve \( \sqrt{81x} - 2 = 7 \)?

**Tip:** When isolating square roots, remember to always check if squaring both sides introduces any extraneous solutions.

Learn how to solve the equation √100x - 1 = 9 with a detailed step-by-step solution. This problem involves key algebraic concepts, including isolating square roots and solving linear equations. Suitable for students in Grades 8-10.

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