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.