To solve the expression:

\[
\sqrt{24} + \sqrt{54} - \sqrt{96}
\]

we start by simplifying each square root.

1. **Simplifying \( \sqrt{24} \):**
   \[
   \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
   \]

2. **Simplifying \( \sqrt{54} \):**
   \[
   \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}
   \]

3. **Simplifying \( \sqrt{96} \):**
   \[
   \sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}
   \]

Now we substitute these simplified forms back into the original expression:

\[
2\sqrt{6} + 3\sqrt{6} - 4\sqrt{6}
\]

Combine like terms:

\[
(2 + 3 - 4)\sqrt{6} = 1\sqrt{6} = \sqrt{6}
\]

Thus, the simplified expression is:

\[
\sqrt{6}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you simplify \( \sqrt{50} + \sqrt{18} \)?
2. Can you explain how to simplify square roots that are not perfect squares?
3. What is the difference between simplifying \( \sqrt{75} \) and \( \sqrt{45} \)?
4. How would you simplify \( 2\sqrt{8} - 3\sqrt{2} + \sqrt{32} \)?
5. How can you estimate the value of \( \sqrt{6} \) without a calculator?

**Tip**: When simplifying square roots, always check if you can break the number into a product of a perfect square and another factor!

Simplify the expression: \( \sqrt{24} + \sqrt{54} - \sqrt{96} \)

Learn how to simplify the radical expression √24 + √54 - √96. This step-by-step solution involves simplifying square roots and combining like terms. Ideal for students in Grades 8-10.

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