Let's simplify the expression:

\[
18\sqrt{2} + 10\sqrt{7} - 5\sqrt{2} - 9\sqrt{7}
\]

1. Combine the terms with \(\sqrt{2}\):
\[
(18\sqrt{2} - 5\sqrt{2}) = 13\sqrt{2}
\]

2. Combine the terms with \(\sqrt{7}\):
\[
(10\sqrt{7} - 9\sqrt{7}) = 1\sqrt{7}
\]

Now, putting it all together:
\[
13\sqrt{2} + \sqrt{7}
\]

So, the simplified expression is:

\[
13\sqrt{2} + \sqrt{7}
\]

Would you like further details or explanations on this? Here are five related questions to deepen your understanding:

1. How do we combine terms with square roots?
2. What is the importance of simplifying radical expressions?
3. Can you simplify \( 3\sqrt{5} + 7\sqrt{5} \)?
4. What happens if you try to add different radicals like \( \sqrt{3} + \sqrt{5} \)?
5. Can square roots ever be simplified further, like \( \sqrt{18} \)?

**Tip:** When simplifying expressions involving square roots, only like terms (with the same radical part) can be combined.

Learn how to simplify the radical expression 18√2 + 10√7 - 5√2 - 9√7. This problem covers important algebraic concepts such as combining like terms with square roots. Suitable for students in Grades 8-10.

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