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

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

t

is irrational. Which statement about

t - 5

is true?

\newline

Choices:

\newline

(A)

t - 5

is rational.

\newline

(B)

t - 5

is irrational.

\newline

(C)

t - 5

can be rational or irrational, depending on the value of

t

.

Identify Number Nature: Identify the nature of the number $5$ . $5$ is a rational number because it can be expressed as a fraction $\frac{5}{1}$ .
Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. Subtracting a rational number from an irrational number results in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a fraction.
Apply Concept to Problem: Apply the concept to the given problem. $\newline$ Since $t$ is irrational and $5$ is rational, $t - 5$ will also be irrational. This is because the subtraction of a rational number from an irrational number does not change the irrational nature of the original number.

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