Irrational numbers are numbers that cannot be expressed as a simple fraction, meaning they cannot be represented as the ratio of two integers. Their decimal representations are non-repeating and non-terminating. Here are some well-known irrational numbers along with their approximate values:
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√2 (Square root of 2)
- Approximate value: 1.414
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π (Pi)
- Approximate value: 3.14159
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e (Euler's number)
- Approximate value: 2.71828
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√3 (Square root of 3)
- Approximate value: 1.732
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√5 (Square root of 5)
- Approximate value: 2.236
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√7 (Square root of 7)
- Approximate value: 2.646
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√11 (Square root of 11)
- Approximate value: 3.317
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φ (Golden ratio, approximately 1.618)
- Approximate value: 1.61803
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√6 (Square root of 6)
- Approximate value: 2.449
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√10 (Square root of 10)
- Approximate value: 3.162
These values are often used in mathematics, science, and engineering, where exact values are not feasible due to their irrational nature but estimates are needed for calculations.
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