simply and combine like radicals. assume all variables represent positive numbers. square root 12 - square root 24

To simplify and combine like radicals for \(\sqrt{12} - \(\sqrt{24}\), follow these steps:

1. **Simplify the square roots:**

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

\[
\sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}
\]

So, we have:

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

2. **Combine the simplified radicals:**

Since \(\sqrt{3}\) and \(\sqrt{6}\) are different, they cannot be combined further.

Thus, the simplified form of \(\sqrt{12} - \sqrt{24}\) is:

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

If you have any questions or need further details, feel free to ask!

Here are 5 more questions you might consider asking:
1. How do you simplify radicals involving variables?
2. What are the properties of radicals that help in simplification?
3. How do you rationalize the denominator of a fraction with radicals?
4. Can you explain how to add and subtract radicals?
5. What are some common mistakes to avoid when working with radicals?

**Tip:** When simplifying radicals, always look for the largest perfect square factor to make simplification easier.

Learn how to simplify and combine like radicals for square root 12 minus square root 24 with a detailed step-by-step solution. This problem covers key algebraic concepts, including radicals and their simplification. Suitable for high school students in Grades 9-12.

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