https://file.aiquickdraw.com/mathbot/file/1729108370469do1ju2it.jpg

The given expression is:

\[
10\sqrt{11} - 2\sqrt{44} + 5\sqrt{176}
\]

We need to simplify this expression by breaking down the square roots where possible:

1. **Simplifying \(\sqrt{44}\)**:
   \[
   \sqrt{44} = \sqrt{4 \times 11} = \sqrt{4} \times \sqrt{11} = 2\sqrt{11}
   \]
   Therefore, \(2\sqrt{44} = 2 \times 2\sqrt{11} = 4\sqrt{11}\).

2. **Simplifying \(\sqrt{176}\)**:
   \[
   \sqrt{176} = \sqrt{16 \times 11} = \sqrt{16} \times \sqrt{11} = 4\sqrt{11}
   \]
   Therefore, \(5\sqrt{176} = 5 \times 4\sqrt{11} = 20\sqrt{11}\).

Now, substitute these simplifications into the original expression:

\[
10\sqrt{11} - 4\sqrt{11} + 20\sqrt{11}
\]

Combine like terms (since all terms contain \(\sqrt{11}\)):

\[
(10 - 4 + 20)\sqrt{11} = 26\sqrt{11}
\]

Thus, the simplified expression is:

\[
26\sqrt{11}
\]

Would you like further details or have any questions? Here are 5 related questions:

1. How do you factor numbers to simplify square roots?
2. Can all square roots be simplified?
3. What happens if the terms under the radicals are not similar?
4. How do you combine terms with square roots?
5. What is the importance of identifying perfect squares in radical simplification?

**Tip**: Always try to factor out the largest perfect square when simplifying square roots.

Simplifica al màxim la següent operació amb radicals: 10√11 − 2√44 + 5√176

This problem focuses on simplifying the expression 10√11 − 2√44 + 5√176 by breaking down square roots and combining like terms. Learn step-by-step how to factor under the radicals and simplify the final expression to 26√11. Suitable for students in Grades 8-10.

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