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We are given the equation:

\[
\sqrt{x - 2} = 10
\]

We are asked to find the value of \( 3x \).

### Step 1: Solve for \( x \)

First, square both sides of the equation to eliminate the square root:

\[
\left(\sqrt{x - 2}\right)^2 = 10^2
\]

\[
x - 2 = 100
\]

Now, add 2 to both sides:

\[
x = 102
\]

### Step 2: Calculate \( 3x \)

Now that we know \( x = 102 \), we calculate \( 3x \):

\[
3x = 3 \times 102 = 306
\]

Thus, the value of \( 3x \) is \( \boxed{306} \).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What is the general method to solve an equation with a square root?
2. If \( \sqrt{x + 4} = 12 \), what is the value of \( x \)?
3. How would the solution change if the equation were \( \sqrt{x - 2} = -10 \)?
4. How do you solve equations involving cube roots, like \( \sqrt[3]{x - 5} = 7 \)?
5. If \( x = 100 \), what is the value of \( 5x + 2 \)?

**Tip**: When solving square root equations, always check for extraneous solutions by plugging the result back into the original equation.

If √x - 2 = 10, what is the value of 3x?

Learn how to solve the square root equation √x - 2 = 10 to find the value of 3x. This step-by-step solution explains key concepts in algebra, including square roots and solving basic equations. Suitable for students in Grades 8-10.

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