To identify which numbers are irrational, we should recall that irrational numbers cannot be expressed as a fraction of two integers (i.e., they cannot be represented as p/q, where p and q are integers and q is not zero). Common examples of irrational numbers include non-repeating and non-terminating decimals, and certain square roots.
Let's analyze each option:
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7/18: This is a fraction and can be expressed as a ratio of two integers, so it is a rational number.
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π: Pi is a well-known irrational number, as it cannot be expressed as a fraction.
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√16: The square root of 16 equals 4, which is a whole number (and thus rational).
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√12: The square root of 12 simplifies to 2√3, which is not a perfect square and cannot be expressed as a fraction of two integers, making it an irrational number.
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1.7: This is a terminating decimal and can be expressed as the fraction 17/10, so it is a rational number.
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√80: The square root of 80 simplifies to 4√5, which is not a perfect square and cannot be expressed as a fraction of two integers, making it an irrational number.
Based on this analysis, the three irrational numbers are:
- π
- √12
- √80
1 answer