To simplify \( \sqrt{45} \), we can rewrite it as the product of two square root factors, one of which is a perfect square.
Step 1: First, we notice that \( 45 = 9 \times 5 \). Here, \( 9 \) is a perfect square.
Thus, we can rewrite \( \sqrt{45} \) as: \[ \sqrt{45} = \sqrt{9 \times 5} \]
Step 2: Now, we apply the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \):
\[ \sqrt{45} = \sqrt{9} \times \sqrt{5} \]
Finally, we simplify \( \sqrt{9} \): \[ \sqrt{9} = 3 \]
So we have: \[ \sqrt{45} = 3\sqrt{5} \]
To summarize: \[ \sqrt{45} = 3\sqrt{5} \]
If you need this in the format of:
- \( 45 \sqrt{=}\)
- \( 3\sqrt{5} \)
then we have: \[ \sqrt{45} = 3 \sqrt{5} \]
Let me know if you want to proceed to the next step!