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Classify each number below as a rational number or an irrational number. (a) Is 4π rational or irrational?

Classify each number below as a rational number or an irrational number.
(a) Is 4π rational or irrational?
(b) Is -√49 rational or irrational?
(c) Is 8/17 rational or irrational?
(d) Is 52.6̅ rational or irrational?
(e) Is -√19 rational or irrational?

Answer

  1. Irrational: 4π is irrational because π is an irrational number, and multiplying it by 4 does not change that.

  2. Rational: -√49 is rational because √49 equals 7, which is an integer, and -7 is also rational.

  3. Rational: 8/17 is rational because it is a fraction of two integers.

  4. Rational: 52.6̅ is rational because it is a repeating decimal.

  5. Irrational: -√19 is irrational because √19 is not a perfect square, making it irrational.

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