The number a is irrational. Which statement about a + 5 is true? Choices: (A)a + 5 is rational. (B)a + 5 is irrational. (C)a + 5 can be rational or irrational, depending on the value of a.

Identify Number Nature: Identify the nature of the number 5. 5 is a rational number because it can be expressed as a fraction (5/1).Consider Number Sum: Consider the sum of an irrational number and a rational number. The sum of an irrational number (a) and a rational number (5) is always irrational. This is because adding a rational number to an irrational number cannot result in a number that can be expressed as a fraction.Determine Correct Statement: Determine the statement that correctly describes a + 5. Since a is irrational and 5 is rational, their sum a + 5 must be irrational.

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The number $a$ is irrational. Which statement about $a + 5$ is true? $\newline$ Choices: $\newline$ (A) $a + 5$ is rational. $\newline$ (B) $a + 5$ is irrational. $\newline$ (C) $a + 5$ can be rational or irrational, depending on the value of $a$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

a

is irrational. Which statement about

a + 5

is true?

\newline

Choices:

\newline

(A)

a + 5

is rational.

\newline

(B)

a + 5

is irrational.

\newline

(C)

a + 5

can be rational or irrational, depending on the value of

a

Identify Number Nature: Identify the nature of the number $5$ . $5$ is a rational number because it can be expressed as a fraction $\frac{5}{1}$ .
Consider Number Sum: Consider the sum of an irrational number and a rational number. The sum of an irrational number $a$ and a rational number $5$ is always irrational. This is because adding a rational number to an irrational number cannot result in a number that can be expressed as a fraction.
Determine Correct Statement: Determine the statement that correctly describes $a + 5$ . $\newline$ Since $a$ is irrational and $5$ is rational, their sum $a + 5$ must be irrational.