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

Definition of Irrational Number: We know that π 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.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.Conclusion: Therefore, regardless of the value of the rational number b, the sum π + b will always be irrational.

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

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Math Problems

Precalculus

Properties of operations on rational and irrational numbers

Full solution

Q. The number

b

is rational. Which statement about

\pi + b

is true?

\newline

Choices:

\newline

(A)

\pi + b

is rational.

\newline

(B)

\pi + b

is irrational.

\newline

(C)

\pi + b

can be rational or irrational, depending on the value of

b

Definition of Irrational Number: We know that $\pi$ 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.
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.
Conclusion: Therefore, regardless of the value of the rational number $b$ , the sum $\pi + b$ will always be irrational.