To simplify the square root of 45, follow these steps:

1. Find the prime factorization of 45: $45 = 9 \times 5 = (3^2) \times 5$

2. Now, use the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$

   Apply this to $\sqrt{45}$: $\sqrt{45} = \sqrt{3^2 \times 5} = \sqrt{3^2} \times \sqrt{5}$

3. Simplify further: $\sqrt{3^2} = 3$

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

Thus, the simplified form of $\sqrt{45}$ is $3\sqrt{5}$.

Would you like more details on this or have any other questions?

Here are 5 related questions to explore further:

1. How do you simplify $\sqrt{72}$?
2. What is the square root of 50 in its simplified form?
3. How do you simplify higher-order roots like $\sqrt[3]{54}$?
4. Can all square roots be simplified? Why or why not?
5. What are the steps to rationalize the denominator in $\frac{1}{\sqrt{5}}$?

Tip: When simplifying square roots, always look for perfect squares (e.g., 4, 9, 16) within the number.