To simplify $(\sqrt{5} + \sqrt{2})^2$, we can apply the formula for expanding a binomial square:

$(a + b)^2 = a^2 + 2ab + b^2$

In this case, $a = \sqrt{5}$ and $b = \sqrt{2}$.

Now, applying the formula:

$(\sqrt{5} + \sqrt{2})^2 = (\sqrt{5})^2 + 2(\sqrt{5})(\sqrt{2}) + (\sqrt{2})^2$

Let's calculate each term:

1. $(\sqrt{5})^2 = 5$
2. $2(\sqrt{5})(\sqrt{2}) = 2\sqrt{10}$
3. $(\sqrt{2})^2 = 2$

So, the simplified result is:

$5 + 2\sqrt{10} + 2$

Now combine the constants:

$7 + 2\sqrt{10}$

Thus, $(\sqrt{5} + \sqrt{2})^2 = 7 + 2\sqrt{10}$.

Would you like further explanation or assistance with something else?

Here are some related questions:

1. How do you expand $(\sqrt{5} - \sqrt{2})^2$?
2. How do you simplify $(\sqrt{3} + \sqrt{7})^2$?
3. What is the binomial expansion formula and how is it applied to expressions like $(a + b)^2$?
4. Can you expand $(x + y)^2$ and find a pattern?
5. What is the difference between simplifying square roots and expanding binomial squares?

Tip: When simplifying expressions with square roots, remember that you can often combine like terms (such as constants), but terms involving square roots (like $\sqrt{2}$ and $\sqrt{5}$) can't be combined unless they are the same radical.