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

Identify the nature: Identify the nature of the number e. The number e is known to be an irrational number because it cannot be expressed as a fraction of two integers and its decimal expansion is non-repeating and non-terminating.Consider the addition: Consider the addition of an irrational number (e) and a rational number (s). When an irrational number is added to a rational number, the result is always irrational. This is because the irrational part cannot be canceled out or simplified to result in a rational number.Apply the rule: Apply this rule to e + s. Since e is irrational and s is rational, their sum e + s must be irrational.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. is the base of the natural logarithm. The number

s

is rational. Which statement about

e + s

is true?

\newline

Choices:

\newline

(A)

e + s

is rational.

\newline

(B)

e + s

is irrational.

\newline

(C)

e + s

can be rational or irrational, depending on the value of

s

Identify the nature: Identify the nature of the number $e$ . The number $e$ is known to be an irrational number because it cannot be expressed as a fraction of two integers and its decimal expansion is non-repeating and non-terminating.
Consider the addition: Consider the addition of an irrational number $e$ and a rational number $s$ . When an irrational number is added to a rational number, the result is always irrational. This is because the irrational part cannot be canceled out or simplified to result in a rational number.
Apply the rule: Apply this rule to $e + s$ . $\newline$ Since $e$ is irrational and $s$ is rational, their sum $e + s$ must be irrational.