To solve \((\sqrt{8} + 3)^2\), we can expand it using the binomial theorem or simply by squaring each term:

\[
(\sqrt{8} + 3)^2 = (\sqrt{8})^2 + 2 \cdot \sqrt{8} \cdot 3 + 3^2
\]

Now, let's calculate each term:

1. \((\sqrt{8})^2 = 8\)
2. \(2 \cdot \sqrt{8} \cdot 3 = 6\sqrt{8}\)
3. \(3^2 = 9\)

So the expression becomes:

\[
8 + 6\sqrt{8} + 9
\]

Finally, simplify it:

\[
8 + 9 + 6\sqrt{8} = 17 + 6\sqrt{8}
\]

Thus, the simplified form of \((\sqrt{8} + 3)^2\) is:

\[
17 + 6\sqrt{8}
\]

Do you have any questions or would you like further details? Here are 5 related questions you could explore:

1. How would you simplify \(\sqrt{8}\) further?
2. What if the expression was \((\sqrt{8} - 3)^2\)?
3. How does this method change if you square a binomial with imaginary numbers?
4. What are other forms of binomial expansions?
5. How can you apply this to solve real-world problems involving area?

**Tip:** When expanding binomials, always apply the distributive property or the binomial theorem to avoid errors.

Learn how to simplify the expression (sqrt(8) + 3)^2 using the binomial theorem and square root properties. Step-by-step calculation with detailed explanations included. Suitable for high school students.

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