We are given the expression:

\[
\frac{\sqrt{a} \cdot \sqrt{b}}{3\sqrt{ab}}
\]

Let's simplify this step by step.

### Step 1: Simplify the numerator
The numerator is \(\sqrt{a} \cdot \sqrt{b}\), which can be combined under one square root:

\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} = \sqrt{ab}
\]

### Step 2: Rewrite the expression
Now the expression becomes:

\[
\frac{\sqrt{ab}}{3\sqrt{ab}}
\]

### Step 3: Cancel out \(\sqrt{ab}\)
Since \(\sqrt{ab}\) appears in both the numerator and denominator, we can cancel it out:

\[
\frac{\sqrt{ab}}{3\sqrt{ab}} = \frac{1}{3}
\]

Thus, the simplified expression is:

\[
\boxed{\frac{1}{3}}
\]

Would you like more details or have any questions?

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Here are 5 related questions to extend the concept:
1. How would you simplify \(\frac{\sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}}{3\sqrt{abc}}\)?
2. What happens if you have cube roots instead of square roots in a similar expression?
3. How would you approach \(\frac{\sqrt{x}}{x\sqrt{y}}\)?
4. What is the general rule for combining square roots like \(\sqrt{a} \cdot \sqrt{b}\)?
5. How do you rationalize a denominator that contains a square root?

**Tip**: When simplifying square roots, always check if the terms inside can be combined under a single root sign to simplify the expression further.

Learn how to simplify the algebraic expression √a√b/3√ab step-by-step. This problem involves key algebraic concepts such as simplifying square roots and applying the cancellation law. Ideal for students in Grades 7-10.

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