Let's solve the given problem by simplifying the radical expressions:

1. $\sqrt{9}$:

   • Simplify: $\sqrt{9} = 3$

2. $\sqrt{18}$:

   • Simplify: $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

3. $5\sqrt{12}$:

   • Simplify: $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$, so $5\sqrt{12} = 5 \times 2\sqrt{3} = 10\sqrt{3}$

Now let's match each expression with the options provided:

• $\sqrt{9} = 3$
• $\sqrt{18} = 3\sqrt{2}$
• $5\sqrt{12} = 10\sqrt{3}$

Matches:

• $\sqrt{9}$ → $3$
• $\sqrt{18}$ → $3\sqrt{2}$
• $5\sqrt{12}$ → $10\sqrt{3}$

Would you like further details or explanations on any of these steps?

Here are 5 related questions you could explore:

1. How do you simplify square roots involving prime factorization?
2. What are the rules for simplifying radical expressions?
3. How do you multiply and simplify expressions involving radicals?
4. What is the process for rationalizing denominators with radicals?
5. How do you handle addition and subtraction of radical expressions?

Tip: When simplifying radicals, always look for perfect squares inside the radical to factor out.