The number u is irrational. Which statement about u + 4 is true? Choices: (A)u + 4 is rational. (B)u + 4 is irrational. (C)u + 4 can be rational or irrational, depending on the value of u.

Identify Number 4: Identify the nature of the number 4. 4 is a whole number, and any whole number is a rational number.Consider Sum: Consider the sum of an irrational number and a rational number. The sum of an irrational number u and a rational number 4 will always be irrational. This is because adding a rational number to an irrational number cannot result in a number that can be expressed as a ratio of two integers.Determine Correct Choice: Determine the correct choice based on the sum of u and 4. Since u is irrational and 4 is rational, their sum u + 4 must be irrational. Therefore, the correct choice is (B) u + 4 is irrational.

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The number $u$ is irrational. Which statement about $u + 4$ is true? $\newline$ Choices: $\newline$ (A) $u + 4$ is rational. $\newline$ (B) $u + 4$ is irrational. $\newline$ (C) $u + 4$ can be rational or irrational, depending on the value of $u$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

u

is irrational. Which statement about

u + 4

is true?

\newline

Choices:

\newline

(A)

u + 4

is rational.

\newline

(B)

u + 4

is irrational.

\newline

(C)

u + 4

can be rational or irrational, depending on the value of

u

Identify Number $4$ : Identify the nature of the number $4$ . $4$ is a whole number, and any whole number is a rational number.
Consider Sum: Consider the sum of an irrational number and a rational number. The sum of an irrational number $u$ and a rational number $4$ will always be irrational. This is because adding a rational number to an irrational number cannot result in a number that can be expressed as a ratio of two integers.
Determine Correct Choice: Determine the correct choice based on the sum of $u$ and $4$ . $\newline$ Since $u$ is irrational and $4$ is rational, their sum $u + 4$ must be irrational. Therefore, the correct choice is (B) $u + 4$ is irrational.