To simplify the expression $\sqrt{8} + \sqrt{50}$:

Step 1: Simplify each square root

1. $\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$
2. $\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2}$

Step 2: Combine like terms

Since both terms have $\sqrt{2}$, they can be combined: $\sqrt{8} + \sqrt{50} = 2\sqrt{2} + 5\sqrt{2} = 7\sqrt{2}$

Final Answer:

$7\sqrt{2}$

Would you like me to explain further or provide additional examples?

Questions for deeper exploration:

1. How can you determine if a square root can be simplified?
2. What are the rules for combining like terms involving radicals?
3. How is $\sqrt{n}$ simplified when $n$ is not a perfect square?
4. What is the geometric interpretation of $\sqrt{n}$?
5. Can you generalize the process for adding and subtracting square roots with different radicands?

Tip:

Always look for the largest perfect square factor when simplifying square roots.