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

Identify Number Type: Identify whether e is a rational or irrational number. The number e (approximately 2.71828) is known to be an irrational number.Properties of Irrational Numbers: Consider the properties of irrational numbers. The sum of an irrational number and a rational number is always irrational. However, the sum of two irrational numbers can be either rational or irrational, depending on the specific numbers.Analyze Statements for e and w: Analyze the given statements with respect to e and w. Since e is irrational and w is also given as irrational, their sum e + w could be either rational or irrational. It depends on the specific value of w. For example, if w were the negative of e, then their sum would be 0, which is rational. However, if w is any irrational number not specifically related to e in such a way that their sum is rational, then e + w would 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 $w$ is irrational. Which statement about $e + w$ is true? $\newline$ Choices: $\newline$ (A) $e + w$ is rational. $\newline$ (B) $e + w$ is irrational. $\newline$ (C) $e + w$ can be rational or irrational, depending on the value of $w$ .

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

w

is irrational. Which statement about

e + w

is true?

\newline

Choices:

\newline

(A)

e + w

is rational.

\newline

(B)

e + w

is irrational.

\newline

(C)

e + w

can be rational or irrational, depending on the value of

w

Identify Number Type: Identify whether $e$ is a rational or irrational number. $\newline$ The number $e$ (approximately $2.71828$ ) is known to be an irrational number.
Properties of Irrational Numbers: Consider the properties of irrational numbers. The sum of an irrational number and a rational number is always irrational. However, the sum of two irrational numbers can be either rational or irrational, depending on the specific numbers.
Analyze Statements for $e$ and $w$ : Analyze the given statements with respect to $e$ and $w$ . Since $e$ is irrational and $w$ is also given as irrational, their sum $e + w$ could be either rational or irrational. It depends on the specific value of $w$ . For example, if $w$ were the negative of $e$ , then their sum would be $w$ $0$ , which is rational. However, if $w$ is any irrational number not specifically related to $e$ in such a way that their sum is rational, then $e + w$ would be irrational.