Math Problem Statement
Solution
Let's evaluate the numbers in the list to identify which one(s) are irrational:
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√64: The square root of 64 is 8, a whole number. Hence, it's a rational number.
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1/64: This is a fraction, which is a ratio of two integers. Therefore, it is a rational number.
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√3: The square root of 3 cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating. Therefore, it is an irrational number.
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√28: This simplifies to √(4 × 7) = 2√7. Since √7 is irrational, √28 is also an irrational number.
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√4: The square root of 4 is 2, a whole number. Hence, it's a rational number.
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23.157: This is a terminating decimal, so it can be expressed as a fraction (23157/1000). Therefore, it is a rational number.
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-64: This is an integer, which can be written as a fraction (-64/1), so it is a rational number.
Conclusion:
The irrational numbers in the list are:
- √3
- √28
Would you like more details on this explanation, or have any questions?
Relative Questions:
- What is the difference between rational and irrational numbers?
- How do you simplify square roots like √28 into more manageable forms?
- Why are terminating and repeating decimals considered rational numbers?
- What are some real-life examples where irrational numbers are used?
- How do you prove whether a number is irrational?
Tip:
When working with square roots, simplify them whenever possible to better identify if the result is rational or irrational.
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Math Problem Analysis
Mathematical Concepts
Rational and Irrational Numbers
Square Roots
Formulas
Simplification of Square Roots
Theorems
Properties of Rational and Irrational Numbers
Suitable Grade Level
Grades 6-8
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