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

Full solution

Q. The number bb is rational. Which statement about π+b\pi + b is true?\newlineChoices:\newline(A) π+b\pi + b is rational.\newline(B) π+b\pi + b is irrational.\newline(C) π+b\pi + b can be rational or irrational, depending on the value of bb.
  1. Definition of Irrational Number: We know that π\pi is an irrational number, which means it cannot be expressed as a fraction of two integers. A rational number, on the other hand, can be expressed as a fraction of two integers.
  2. Sum of Irrational and Rational Numbers: When we add an irrational number to a rational number, the sum is always irrational. This is because the irrational part cannot be expressed as a fraction, and thus the entire sum cannot be expressed as a fraction of two integers.
  3. Conclusion: Therefore, regardless of the value of the rational number bb, the sum π+b\pi + b will always be irrational.

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