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The number $c$ is irrational. Which statement about $c + 10$ is true? $\newline$ Choices: $\newline$ (A) $c + 10$ is rational. $\newline$ (B) $c + 10$ is irrational. $\newline$ (C) $c + 10$ can be rational or irrational, depending on the value of $c$ .

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

c

is irrational. Which statement about

c + 10

is true?

\newline

Choices:

\newline

(A)

c + 10

is rational.

\newline

(B)

c + 10

is irrational.

\newline

(C)

c + 10

can be rational or irrational, depending on the value of

c

.

Identify Number Nature: Identify the nature of the number $10$ . $10$ is an integer, and all integers are rational numbers.
Consider Number Sum: Consider the sum of an irrational number and a rational number. The sum of an irrational number $c$ and a rational number $10$ is always irrational.
Determine Truth: Determine the truth of the given statements based on the previous step. $\newline$ Since $c$ is irrational and $10$ is rational, their sum $c + 10$ must be irrational. $\newline$ Therefore, the correct statement is (B) $c + 10$ is irrational.

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