To simplify $\sqrt{45}$, we perform the following steps:

1. Factorize 45 into prime factors:
   $45 = 3^2 \times 5$

2. Apply the square root property:
   $\sqrt{45} = \sqrt{3^2 \times 5} = \sqrt{3^2} \times \sqrt{5} = 3\sqrt{5}$

Final simplified result:
$\sqrt{45} = 3\sqrt{5}$

Let me know if you would like further clarification or have any other questions!

Related Questions:

1. What is the prime factorization of 45 and how does it simplify the square root?
2. How do you simplify other square roots like $\sqrt{72}$ or $\sqrt{50}$?
3. What are perfect squares, and how do they help in simplifying square roots?
4. Can you convert $3\sqrt{5}$ into a decimal approximation?
5. What is the general method for simplifying square roots?

Tip:

Always check for the largest perfect square factor when simplifying square roots to make the process faster.