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

Identify π nature: Identify the nature of π. π is a well-known mathematical constant that is irrational.Consider sum with s: Consider the sum of a rational number s and an irrational number π. Since s is rational and π is irrational, their sum s + π will also be irrational. This is because the sum of a rational and an irrational number is always irrational.Check for exceptions: Check for any exceptions that could make s + π rational. There are no values of s that could make s + π rational, because no matter what rational number you add to π, the sum will remain irrational.Conclude correct statement: Conclude the correct statement from the given choices. The correct statement about s + π is that it is irrational.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

s

is rational. Which statement about

s + \pi

is true?

\newline

Choices:

\newline

(A)

s + \pi

is rational.

\newline

(B)

s + \pi

is irrational.

\newline

(C)

s + \pi

can be rational or irrational, depending on the value of

s

Identify $\pi$ nature: Identify the nature of $\pi$ . $\newline$ $\pi$ is a well-known mathematical constant that is irrational.
Consider sum with $s$ : Consider the sum of a rational number $s$ and an irrational number $\pi$ . Since $s$ is rational and $\pi$ is irrational, their sum $s + \pi$ will also be irrational. This is because the sum of a rational and an irrational number is always irrational.
Check for exceptions: Check for any exceptions that could make $s + \pi$ rational. $\newline$ There are no values of $s$ that could make $s + \pi$ rational, because no matter what rational number you add to $\pi$ , the sum will remain irrational.
Conclude correct statement: Conclude the correct statement from the given choices. $\newline$ The correct statement about $s + \pi$ is that it is irrational.