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Is the following number rational or irrational?

-2pi
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational?\newline2π-2\pi\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational

Full solution

Q. Is the following number rational or irrational?\newline2π-2\pi\newlineChoose 11 answer:\newline(A) Rational\newline(B) Irrational
  1. Evaluate extpi: Evaluate the nature of extpi.\newline extPi ( extpi) is a well-known mathematical constant that represents the ratio of the circumference of a circle to its diameter. extPi is an irrational number because it cannot be expressed as a fraction of two integers; its decimal representation is non-terminating and non-repeating.
  2. Determine 2π-2\pi: Determine the nature of 2π-2\pi.\newlineMultiplying an irrational number by a rational number (in this case, 2-2) does not change its irrational nature. The product of a rational and an irrational number is always irrational.
  3. Conclude -2\pi \'s nature: Conclude whether \$ -2\pi is rational or irrational.\newlineSince π \pi is irrational, and multiplying by 2 -2 does not change this, 2π -2\pi is also irrational.

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