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.

Learn how to simplify the square root of 45 by applying prime factorization and properties of square roots. This detailed guide covers the steps to break down the number into prime factors and simplify the expression to 3√5. Suitable for students in Grades 7-9.

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