If and , find the value of and determine if the result is rational or irrational. The value of is ________, and it is ________.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to simplify expressions involving square roots and determine if the result is rational or irrational. It requires understanding the properties of irrational numbers and how they behave under division.
Key Concept Explanation
Irrational numbers cannot be expressed as a ratio of two integers and have non-terminating, non-repeating decimal expansions. Operations with irrational numbers, such as division, generally result in irrational numbers unless the quotient simplifies to a rational number.
Step-by-step Solution
1. Substitute the given values: , .
2. Divide the values:
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