https://file.aiquickdraw.com/mathbot/file/1726171310741hcbymsyx.jpg

The image shows the following mathematical expression:

\[
\sqrt{3} \cdot \frac{2a+b}{3b} = \frac{27a}{9b}
\]

This appears to be an equation. Let's solve it step by step:

1. **Simplify the right-hand side (RHS):**
   \[
   \frac{27a}{9b} = 3 \cdot \frac{a}{b}
   \]

2. Now we have the equation:
   \[
   \sqrt{3} \cdot \frac{2a + b}{3b} = 3 \cdot \frac{a}{b}
   \]

3. **Multiply both sides by \(3b\) to eliminate the denominator:**
   \[
   \sqrt{3}(2a + b) = 9a
   \]

4. **Distribute \(\sqrt{3}\) on the left-hand side (LHS):**
   \[
   \sqrt{3} \cdot 2a + \sqrt{3} \cdot b = 9a
   \]

At this point, the equation becomes:
\[
2a\sqrt{3} + b\sqrt{3} = 9a
\]

Now, if you want to solve for \(b\) or \(a\), further manipulation depends on whether any variables need to be isolated.

Would you like to proceed with solving for a specific variable, or need further clarification on any step? 

Here are five related questions you could explore:
1. How can we further simplify expressions involving square roots?
2. What happens if we solve for \(b\) in terms

Solve the equation involving square roots: \( \sqrt{3} \cdot \frac{2a+b}{3b} = \frac{27a}{9b} \)

Learn how to solve an equation involving square roots and fractions: \( \sqrt{3} \cdot \frac{2a+b}{3b} = \frac{27a}{9b} \). This detailed step-by-step solution covers algebraic concepts, simplifying square roots, and solving for variables. Suitable for students in Grades 9-11.

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