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Square the expression. Write your answer in simplest form.


The expression you provided is \((\sqrt{2} + \sqrt{13})^2\). To square this expression, we can use the formula for the square of a binomial:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \( a = \sqrt{2} \) and \( b = \sqrt{13} \).

Let's break this down:

1. \( a^2 = (\sqrt{2})^2 = 2 \)
2. \( b^2 = (\sqrt{13})^2 = 13 \)
3. \( 2ab = 2(\sqrt{2})(\sqrt{13}) = 2\sqrt{26} \)

Now, combine these results:

\[
(\sqrt{2} + \sqrt{13})^2 = 2 + 13 + 2\sqrt{26} = 15 + 2\sqrt{26}
\]

So, the expression simplifies to:

\[
\boxed{15 + 2\sqrt{26}}
\]

Would you like any additional details or have any questions?

### Related Questions:
1. What is the general formula for squaring a binomial?
2. How would you square a binomial if it contains a negative sign, such as \((\sqrt{5} - \sqrt{7})^2\)?
3. Can this problem be solved by expanding the expression directly without using a formula?
4. How do you simplify expressions involving square roots, like \( \sqrt{26} \)?
5. What would be the steps to solve \((\sqrt{3} + \sqrt{11})^2\)?
6. How does the distributive property apply to squaring binomials?
7. What are some common mistakes to avoid when squaring expressions with radicals?
8. How does this problem relate to solving quadratic equations?

### Tip:
When squaring binomials with radicals, always ensure to simplify the square roots first if possible, and then carefully apply the binomial square formula.

Learn how to square the expression (sqrt(2) + sqrt(13))^2 and simplify it to 15 + 2*sqrt(26). This problem involves binomial expansion, square roots, and simplification of radicals. Suitable for high school students.

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