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To simplify the expression:

\[
19\sqrt{11} + 25\sqrt{2} + 8\sqrt{11} + 23\sqrt{2}
\]

We can group the like terms (terms with \(\sqrt{11}\) and terms with \(\sqrt{2}\)):

\[
(19\sqrt{11} + 8\sqrt{11}) + (25\sqrt{2} + 23\sqrt{2})
\]

This simplifies to:

\[
(19 + 8)\sqrt{11} + (25 + 23)\sqrt{2}
\]

\[
= 27\sqrt{11} + 48\sqrt{2}
\]

Thus, the simplified expression is:

\[
27\sqrt{11} + 48\sqrt{2}
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Can you simplify \(15\sqrt{3} + 10\sqrt{3} - 5\sqrt{3}\)?
2. How would you combine \(12\sqrt{5} + 7\sqrt{7} - 4\sqrt{5}\)?
3. Can \(3\sqrt{6} + 2\sqrt{6}\) be simplified? If so, how?
4. What happens if you add \(5\sqrt{7} + 9\sqrt{11} + 3\sqrt{7}\)?
5. How would you approach simplifying an expression like \(6\sqrt{2} + 3\sqrt{8}\)?

**Tip**: When simplifying radicals, always look to combine like terms that have the same square root component.

Simplify: 19√11 + 25√2 + 8√11 + 23√2

Learn how to simplify the radical expression 19√11 + 25√2 + 8√11 + 23√2 by combining like terms. This example demonstrates key algebraic concepts, such as handling radicals and simplifying expressions. Ideal for students in Grades 9-11.

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