The number p is irrational. Which statement about p - 8 is true? Choices: (A)p - 8 is rational. (B)p - 8 is irrational. (C)p - 8 can be rational or irrational, depending on the value of p.

Identify Number 8: Identify the nature of the number 8. 8 is a whole number, and all whole numbers are rational numbers.Subtract Rational from Irrational: Understand 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 ratio of two integers.Apply to Given Problem: Apply the understanding to the given problem. Since p is irrational and 8 is rational, p - 8 will also be irrational.

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The number $p$ is irrational. Which statement about $p - 8$ is true? $\newline$ Choices: $\newline$ (A) $p - 8$ is rational. $\newline$ (B) $p - 8$ is irrational. $\newline$ (C) $p - 8$ can be rational or irrational, depending on the value of $p$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

p

is irrational. Which statement about

p - 8

is true?

\newline

Choices:

\newline

(A)

p - 8

is rational.

\newline

(B)

p - 8

is irrational.

\newline

(C)

p - 8

can be rational or irrational, depending on the value of

p

Identify Number $8$ : Identify the nature of the number $8$ . $8$ is a whole number, and all whole numbers are rational numbers.
Subtract Rational from Irrational: Understand 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 ratio of two integers.
Apply to Given Problem: Apply the understanding to the given problem. $\newline$ Since $p$ is irrational and $8$ is rational, $p - 8$ will also be irrational.