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The number $c$ is irrational. Which statement about $c - 3$ is true? $\newline$ Choices: $\newline$ (A) $c - 3$ is rational. $\newline$ (B) $c - 3$ is irrational. $\newline$ (C) $c - 3$ 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 - 3

is true?

\newline

Choices:

\newline

(A)

c - 3

is rational.

\newline

(B)

c - 3

is irrational.

\newline

(C)

c - 3

can be rational or irrational, depending on the value of

c

.

Understand Number $3$ : Understand the nature of the number $3$ . $\newline$ The number $3$ is a rational number because it can be expressed as a fraction $(\frac{3}{1})$ .
Subtract Rational from Irrational: Analyze the subtraction of a rational number from an irrational number. $\newline$ When you subtract a rational number from an irrational number, the result is always an irrational number. This is because if the result were rational, then adding the rational number back to it would yield the original irrational number, which is a contradiction.
Apply Analysis to Problem: Apply the analysis to the given problem. $\newline$ Since $c$ is irrational and $3$ is rational, $c - 3$ must be irrational.

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