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

Identify Number Type: Identify whether e is a rational or irrational number. e is the base of the natural logarithm and is known to be an irrational number.Given Information: We know: u is a rational number. e is an irrational number. Consider the nature of the sum u + e. The sum of a rational number and an irrational number is always irrational.Consider Sum Nature: Therefore, no matter what rational value u has, the sum u + e will always be irrational. This is because the irrational part (e) cannot be expressed as a ratio of two integers, and adding a rational number to it does not change this fact.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

u

is rational.

e

is the base of the natural logarithm. Which statement about

u + e

is true?

\newline

Choices:

\newline

(A)

u + e

is rational.

\newline

(B)

u + e

is irrational.

\newline

(C)

u + e

can be rational or irrational, depending on the value of

u

Identify Number Type: Identify whether $e$ is a rational or irrational number. $e$ is the base of the natural logarithm and is known to be an irrational number.
Given Information: We know: $\newline$ $u$ is a rational number. $\newline$ $e$ is an irrational number. $\newline$ Consider the nature of the sum $u + e$ . $\newline$ The sum of a rational number and an irrational number is always irrational.
Consider Sum Nature: Therefore, no matter what rational value $u$ has, the sum $u + e$ will always be irrational. $\newline$ This is because the irrational part ( $e$ ) cannot be expressed as a ratio of two integers, and adding a rational number to it does not change this fact.