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Step 1:I'll solve this step-by-step using precise LaTeX formatting:
Step 2:: Identify the number under the square root
- We have $$\sqrt{32}$$ to simplify
Step 3:: Find the largest perfect square factor of 32
- The largest perfect square factor is $$2^{4} = 16
- Break down 32 into its prime factorization
Step 4:: Rewrite the square root
- $$\sqrt{32} = \sqrt{16 \times 2}
- \sqrt{32} = \sqrt{16} \times \sqrt{2}
Step 5:: Simplify
- $$\sqrt{16} = 4
- \sqrt{32} = 4\sqrt{2}
Final Answer
Key Insights: - Always look for perfect square factors inside the radical - Separate the perfect square factor from the remaining term - Simplify the perfect square factor outside the radical
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