Question #6450746Fill in the Blank
Algebra-2
Question
Simplify the expression (). The simplified form is ___________.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the ability to simplify a radical expression by dividing the radicands and then simplifying the result, including handling higher-order roots.
This problem assesses the ability to simplify a radical expression by dividing the radicands and then simplifying the result, including handling higher-order roots.
Key Concept Explanation
When dividing two radicals with the same index, the index remains unchanged. The quotient of the numerator’s radicand and the denominator’s radicand becomes the new radicand. Higher-order roots (e.g., fourth roots) are handled similarly to square and cube roots.
When dividing two radicals with the same index, the index remains unchanged. The quotient of the numerator’s radicand and the denominator’s radicand becomes the new radicand. Higher-order roots (e.g., fourth roots) are handled similarly to square and cube roots.
Step-by-step Solution
1. Separate the coefficients and the radicals:
2. Simplify the fraction inside the radical:
3. Simplify the radical:
1. Separate the coefficients and the radicals:
2. Simplify the fraction inside the radical:
3. Simplify the radical:
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