The given expression is $(\sqrt{3} + \sqrt{7})^2$. Let’s expand and simplify it.

Step-by-Step Solution:

Using the expansion formula $(a + b)^2 = a^2 + 2ab + b^2$:

$(\sqrt{3} + \sqrt{7})^2 = (\sqrt{3})^2 + 2(\sqrt{3})(\sqrt{7}) + (\sqrt{7})^2$

1. $(\sqrt{3})^2 = 3$
2. $(\sqrt{7})^2 = 7$
3. $2(\sqrt{3})(\sqrt{7}) = 2\sqrt{21}$

Now, combine the terms:

$(\sqrt{3} + \sqrt{7})^2 = 3 + 7 + 2\sqrt{21}$

$= 10 + 2\sqrt{21}$

Final Answer:

$10 + 2\sqrt{21}$

Let me know if you want further clarification!

Here are some related questions for practice:

1. Expand and simplify $(\sqrt{5} + \sqrt{2})^2$.
2. Expand and simplify $(\sqrt{3} - \sqrt{7})^2$.
3. Solve for $(\sqrt{3} + \sqrt{7})(\sqrt{3} - \sqrt{7})$.
4. Expand and simplify $(a + b)^2$ for general variables $a$ and $b$.
5. Solve for the value of $x^2 + 2x + 1$ when $x = \sqrt{3} + \sqrt{7}$.

Tip:

When working with square root terms, always check for perfect squares to simplify the results.