Let's solve the expression step by step:

$(\sqrt{2} + \sqrt{5}) + (\sqrt{2} - \sqrt{5})$

Step 1: Group the like terms

We can combine the terms with $\sqrt{2}$ and the terms with $\sqrt{5}$:

$(\sqrt{2} + \sqrt{2}) + (\sqrt{5} - \sqrt{5})$

Step 2: Simplify

• $\sqrt{2} + \sqrt{2} = 2\sqrt{2}$
• $\sqrt{5} - \sqrt{5} = 0$

Thus, the expression becomes:

$2\sqrt{2} + 0 = 2\sqrt{2}$

Final Answer:

$2\sqrt{2}$

Would you like further explanation or assistance with another problem? Here are some related questions:

1. What happens if you subtract the two terms instead of adding them?
2. How do you simplify expressions with square roots of numbers that can't be simplified further?
3. Can you express $2\sqrt{2}$ as a decimal approximation?
4. What is the result if you multiply $\sqrt{2}$ and $\sqrt{5}$?
5. How do you handle sums or differences of square roots in other algebraic expressions?

Tip: When adding or subtracting square roots, only like terms can be combined—just as with regular variables like $x$ or $y$.