Let's simplify each term first:

1. $8\sqrt{8}$:
   Break down $\sqrt{8}$ as follows:
   $\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$
   Now, substitute back into $8\sqrt{8}$:
   $8\sqrt{8} = 8 \times 2\sqrt{2} = 16\sqrt{2}$

2. $3\sqrt{2}$:
   This term is already simplified.

3. $3\sqrt{12}$:
   Break down $\sqrt{12}$ as follows:
   $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$
   Now, substitute back into $3\sqrt{12}$:
   $3\sqrt{12} = 3 \times 2\sqrt{3} = 6\sqrt{3}$

Now, putting it all together: $8\sqrt{8} + 3\sqrt{2} + 3\sqrt{12} = 16\sqrt{2} + 3\sqrt{2} + 6\sqrt{3}$

Combine like terms: $(16\sqrt{2} + 3\sqrt{2}) + 6\sqrt{3} = 19\sqrt{2} + 6\sqrt{3}$

Thus, the simplified expression is: $19\sqrt{2} + 6\sqrt{3}$

Would you like more details on the simplification process or another explanation?

Here are 5 related questions:

1. How would you simplify $5\sqrt{18} + 2\sqrt{8}$?
2. What is $\sqrt{50} + \sqrt{2}$?
3. How do you factor and simplify $\sqrt{72}$?
4. What is the result of combining $7\sqrt{3} + 2\sqrt{12}$?
5. How do you simplify $4\sqrt{32} + 5\sqrt{2}$?

Tip: Always look for perfect squares within the square root to simplify expressions efficiently!