Question #6450508Fill in the Blank
Algebra-2
Question
Simplify the expression , where . The simplified form is _________.
Answer & Analysis
Analysis
Question Analysis
This problem tests the student's ability to simplify a fourth root expression by factoring the radicand and applying the properties of radicals.
This problem tests the student's ability to simplify a fourth root 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 fourth roots, this means no factors that are perfect fourth powers.
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 fourth roots, this means no factors that are perfect fourth powers.
Step-by-step Solution
1. Factor the radicand into a product of a perfect fourth power and another factor:
2. Recognize that and , both of which are perfect fourth powers.
3. Apply the property of radicals for products:
1. Factor the radicand into a product of a perfect fourth power and another factor:
2. Recognize that and , both of which are perfect fourth powers.
3. Apply the property of radicals for products:
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