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The number ss is rational. Which statement about s+πs + \pi is true?\newlineChoices:\newline(A) s+πs + \pi is rational.\newline(B) s+πs + \pi is irrational.\newline(C) s+πs + \pi can be rational or irrational, depending on the value of ss.

Full solution

Q. The number ss is rational. Which statement about s+πs + \pi is true?\newlineChoices:\newline(A) s+πs + \pi is rational.\newline(B) s+πs + \pi is irrational.\newline(C) s+πs + \pi can be rational or irrational, depending on the value of ss.
  1. Identify π\pi nature: Identify the nature of π\pi.\newlineπ\pi is a well-known mathematical constant that is irrational.
  2. Consider sum with ss: Consider the sum of a rational number ss and an irrational number π\pi. Since ss is rational and π\pi is irrational, their sum s+πs + \pi will also be irrational. This is because the sum of a rational and an irrational number is always irrational.
  3. Check for exceptions: Check for any exceptions that could make s+πs + \pi rational.\newlineThere are no values of ss that could make s+πs + \pi rational, because no matter what rational number you add to π\pi, the sum will remain irrational.
  4. Conclude correct statement: Conclude the correct statement from the given choices.\newlineThe correct statement about s+πs + \pi is that it is irrational.

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