Math Problem Statement

Which number in the list is/are an irrational number? 1. √64 2. 1/64 3. √3 4. √28 5. √4 6. 23.157 7. -64

Solution

Let's evaluate the numbers in the list to identify which one(s) are irrational:

  1. √64: The square root of 64 is 8, a whole number. Hence, it's a rational number.

  2. 1/64: This is a fraction, which is a ratio of two integers. Therefore, it is a rational number.

  3. √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.

  4. √28: This simplifies to √(4 × 7) = 2√7. Since √7 is irrational, √28 is also an irrational number.

  5. √4: The square root of 4 is 2, a whole number. Hence, it's a rational number.

  6. 23.157: This is a terminating decimal, so it can be expressed as a fraction (23157/1000). Therefore, it is a rational number.

  7. -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:

  1. What is the difference between rational and irrational numbers?
  2. How do you simplify square roots like √28 into more manageable forms?
  3. Why are terminating and repeating decimals considered rational numbers?
  4. What are some real-life examples where irrational numbers are used?
  5. 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