Simplify the expressionby factoring it into prime factors and extracting the perfect square. The simplified form is.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to simplify a radical expression by factoring it into prime factors and extracting the perfect square.
Key Concept Explanation
The key concept here is the property of radicals that allows us to factor out perfect squares from the radicand. This is essential for simplifying expressions involving roots.
Step-by-step Solution
1. Factor 243 into its prime factors:
2. Rewrite the radical expression:
3. Extract the perfect square:
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