To simplify $\sqrt{45}$, follow these steps:

1. Find the prime factorization of 45: $45 = 3 \times 3 \times 5 = 3^2 \times 5$

2. Apply the square root property:
   $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$

   So,
   $\sqrt{45} = \sqrt{3^2 \times 5} = \sqrt{3^2} \times \sqrt{5}$

3. Simplify:
   Since $\sqrt{3^2} = 3$, we get
   $\sqrt{45} = 3\sqrt{5}$

Final Answer:

$\sqrt{45} = 3\sqrt{5}$

Would you like a deeper explanation or another example?

Here are five related questions to explore:

1. Simplify $\sqrt{72}$.
2. Simplify $\sqrt{98}$.
3. Express $\sqrt{50}$ in simplest radical form.
4. How do you simplify cube roots, such as $\sqrt[3]{54}$?
5. Explain how to simplify radicals with variables, e.g., $\sqrt{48x^2}$.

Tip: Always look for perfect square factors when simplifying square roots.