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

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

r

is irrational. Which statement about

r + 5

is true?

\newline

Choices:

\newline

(A)

r + 5

is rational.

\newline

(B)

r + 5

is irrational.

\newline

(C)

r + 5

can be rational or irrational, depending on the value of

r

.

Identify Number $5$ : Identify the nature of the number $5$ . $5$ is a whole number, and all whole numbers are rational numbers.
Sum of Numbers: Consider the sum of an irrational number and a rational number. The sum of an irrational number $r$ and a rational number $5$ will always be irrational. This is because adding a rational number to an irrational number does not result in a number that can be expressed as a ratio of two integers.
Truth of Statements: Determine the truth of the given statements based on the sum of $r$ and $5$ . Since $r$ is irrational and $5$ is rational, their sum $r + 5$ cannot be expressed as a ratio of two integers, which means $r + 5$ is irrational.

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