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We are tasked with solving the equation:

\[
\sqrt{w - 3} = 6
\]

### Step-by-Step Solution:

1. **Square both sides** of the equation to eliminate the square root:

\[
(\sqrt{w - 3})^2 = 6^2
\]

This simplifies to:

\[
w - 3 = 36
\]

2. **Add 3** to both sides to solve for \( w \):

\[
w = 36 + 3
\]

\[
w = 39
\]

### Solution:
The value of \( w \) is **39**.

Do you have any questions or want further details? Here are a few related questions for practice:

1. What would the solution be if the square root was set equal to a different number, like 5 instead of 6?
2. What happens if \( w - 3 \) were negative under the square root?
3. How would the solution change if the square root was a cube root instead?
4. Can we solve this equation graphically? How?
5. What if \( w \) were a complex number? How would the solution change?

**Tip:** Always check for extraneous solutions when dealing with square roots!

Solve for w, where w is a real number. \sqrt{w - 3} = 6

Learn how to solve the equation \sqrt{w - 3} = 6 with a step-by-step explanation. This problem covers algebraic techniques like squaring both sides and solving for the unknown. Suitable for students in Grades 8-10.

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