Simplify the expression , where . The simplified form is __________.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the student's ability to simplify a radical expression by factoring the radicand and applying the properties of radicals.
Key Concept Explanation
The goal is to express the radical in its simplest form, where the radicand has no factors that are perfect powers of the index. For square roots, this means no factors that are perfect squares.
Step-by-step Solution
1. Factor the radicand into a product of a perfect square and another factor: , where
2. Recognize that and
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