Identify the irrational number among the following: , , , and . The irrational number is _______.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to recognize irrational numbers. The student must identify which of the given square roots is not a perfect square and therefore is an irrational number.
Key Concept Explanation
Irrational numbers are real numbers that cannot be expressed as a ratio of two integers and have non-terminating, non-repeating decimal expansions. Square roots of non-perfect squares are examples of irrational numbers.
Step-by-step Solution
1. Evaluate each square root:
(rational)
(rational)
(irrational)
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