https://file.aiquickdraw.com/mathbot/file/17281584798109lw93yr7.jpg

Let's simplify the given radical expression:

\[
\sqrt{3} + \sqrt{192}
\]

### Step 1: Simplify \(\sqrt{192}\)
To simplify \(\sqrt{192}\), we need to find the prime factorization of 192.

\[
192 = 2^6 \times 3
\]

So,

\[
\sqrt{192} = \sqrt{2^6 \times 3} = \sqrt{(2^3)^2 \times 3} = 8\sqrt{3}
\]

### Step 2: Combine the terms
Now, the expression becomes:

\[
\sqrt{3} + 8\sqrt{3}
\]

Since both terms have the same radical (\(\sqrt{3}\)), we can combine them:

\[
(1 + 8)\sqrt{3} = 9\sqrt{3}
\]

### Final Answer:
\[
9\sqrt{3}
\]

Would you like further details or have any questions about the steps?

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Here are 5 related questions to deepen your understanding:
1. How do you simplify the square root of any number?
2. What is the process for combining like terms involving radicals?
3. Can all radicals be simplified, or are some already in their simplest form?
4. How would you simplify a radical expression that involves cube roots instead of square roots?
5. What happens if the radicals have different terms inside? Can they still be combined?

**Tip**: Always check if the radicand (the number inside the square root) can be factored into perfect squares to simplify the expression.

Express in simplest radical form: √3 + √192

Learn how to simplify the radical expression √3 + √192 by using prime factorization and combining like terms. This solution covers simplifying radicals and algebraic techniques suitable for students in Grades 8-10.

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