To simplify the expression $\sqrt{2} \cdot \sqrt{3}$, we can use the property of square roots that states:

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$

In this case, $a = 2$ and $b = 3$, so:

$\sqrt{2} \cdot \sqrt{3} = \sqrt{2 \cdot 3} = \sqrt{6}$

Thus, the simplified form is $\sqrt{6}$.

Would you like any further details or clarifications?

Here are some related questions to explore:

1. How can we simplify square roots with more than two factors?
2. What happens if the numbers under the square root are perfect squares?
3. Can square roots be simplified when they have variables under them?
4. How do you multiply square roots when one of them is a fraction?
5. What is the difference between square roots and cube roots in simplification?

Tip: Always look for opportunities to combine square roots when possible to simplify the expression more efficiently.