Let's correct the interpretation for question 22. The expression is:

\[ \sqrt{6x} \cdot \sqrt{3x} \]

To simplify this expression, we can use the property of square roots which states that \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).

Applying this property:

\[ \sqrt{6x} \cdot \sqrt{3x} = \sqrt{(6x) \cdot (3x)} \]

\[ = \sqrt{18x^2} \]

Since \(18x^2\) can be further simplified, we have:

\[ = \sqrt{18} \cdot \sqrt{x^2} \]

\[ = \sqrt{18} \cdot x \]

\[ = 3\sqrt{2} \cdot x \]

Thus, the simplified form is:

\[ 3x\sqrt{2} \]

Would you like more details or have any questions about this solution?

Here are some additional related problems to practice:

1. Simplify \(\sqrt{8x} \cdot \sqrt{2x}\).
2. Simplify \(\sqrt{5x} \cdot \sqrt{4x}\).
3. Simplify \(\sqrt{12x} \cdot \sqrt{3x}\).
4. Simplify \(\sqrt{7x} \cdot \sqrt{2x}\).
5. Simplify \(\sqrt{9x} \cdot \sqrt{3x}\).
6. Simplify \(\sqrt{4x} \cdot \sqrt{6x}\).
7. Simplify \(\sqrt{10x} \cdot \sqrt{5x}\).
8. Simplify \(\sqrt{14x} \cdot \sqrt{2x}\).

**Tip:** Always look for opportunities to use properties of square roots to simplify expressions.

Learn how to simplify the expression \( \sqrt{6x} \cdot \sqrt{3x} \) using the properties of square roots. This problem involves multiplying square roots and simplifying the resulting expression \( 3x\sqrt{2} \). Suitable for high school students studying algebra and square roots.

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