https://file.aiquickdraw.com/mathbot/file/1726507854537irtircxv.jpg

The expression you've provided is:

\[
3 \sqrt{6} \left( \sqrt{7} - \sqrt{2} \right)
\]

To simplify this, let's distribute \( 3 \sqrt{6} \) to both terms inside the parentheses:

\[
= 3 \sqrt{6} \times \sqrt{7} - 3 \sqrt{6} \times \sqrt{2}
\]

We can now multiply the square roots:

\[
= 3 \sqrt{42} - 3 \sqrt{12}
\]

Next, simplify \( \sqrt{12} \):

\[
\sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3}
\]

Thus, the expression becomes:

\[
= 3 \sqrt{42} - 6 \sqrt{3}
\]

So the final simplified expression is:

\[
3 \sqrt{42} - 6 \sqrt{3}
\]

Would you like further clarification on any step or more details?

Here are five related questions to consider:
1. How do you multiply square roots with coefficients?
2. What is the method to simplify a square root like \( \sqrt{12} \)?
3. Can this expression be simplified further by approximating the square roots numerically?
4. What are some common strategies to handle expressions with multiple square roots?
5. What are the real-world applications of simplifying expressions like this?

**Tip:** Always look for perfect squares within a square root to simplify expressions effectively.

Learn how to simplify the expression 3√6(√7 - √2) using the distributive property and properties of square roots. This step-by-step solution covers square root multiplication and simplification for advanced algebra students. Ideal for Grades 9-12.

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