The number z is irrational. Which statement about 2 + z is true? Choices: (A)2 + z is rational. (B)2 + z is irrational. (C)2 + z can be rational or irrational, depending on the value of z.

Identify Number 2: Identify the nature of the number 2. 2 is a rational number because it can be expressed as a fraction of two integers (2/1).Consider Number z: Consider the nature of the number z. z is given as an irrational number, which means it cannot be expressed as a fraction of two integers.Analyze Sum: Analyze the sum of a rational number and an irrational number. The sum of a rational number (2) and an irrational number (z) will always be irrational. This is because if it were rational, then subtracting the rational part (2) from the sum would leave us with a rational number, which contradicts the fact that z is irrational.Conclude Result: Conclude the nature of 2 + z. Since adding a rational number to an irrational number results in an irrational number, the statement that 2 + z is irrational is true.

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The number $z$ is irrational. Which statement about $2 + z$ is true? $\newline$ Choices: $\newline$ (A) $2 + z$ is rational. $\newline$ (B) $2 + z$ is irrational. $\newline$ (C) $2 + z$ can be rational or irrational, depending on the value of $z$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

z

is irrational. Which statement about

2 + z

is true?

\newline

Choices:

\newline

(A)

2 + z

is rational.

\newline

(B)

2 + z

is irrational.

\newline

(C)

2 + z

can be rational or irrational, depending on the value of

z

Identify Number $2$ : Identify the nature of the number $2$ . $2$ is a rational number because it can be expressed as a fraction of two integers $(2/1)$ .
Consider Number $z$ : Consider the nature of the number $z$ . $z$ is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
Analyze Sum: Analyze the sum of a rational number and an irrational number. $\newline$ The sum of a rational number $2$ and an irrational number $z$ will always be irrational. This is because if it were rational, then subtracting the rational part $2$ from the sum would leave us with a rational number, which contradicts the fact that $z$ is irrational.
Conclude Result: Conclude the nature of $2 + z$ . Since adding a rational number to an irrational number results in an irrational number, the statement that $2 + z$ is irrational is true.