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

Identify Number Type: Identify whether the number 8 is a rational or irrational number. 8 is a whole number, and all whole numbers are rational numbers.Determine s - 8: We know: s is an irrational number. 8 is a rational number. Which statement about s - 8 is true? Subtracting a rational number from an irrational number results in an irrational number.Evaluate s - 8: Therefore, s - 8 is irrational, which means that choice (A) is incorrect.Evaluate s + 8: Since adding or subtracting a rational number from an irrational number always results in an irrational number, s + 8 is also irrational, which means that choice (B) is correct.Evaluate s + 8: Choice (C) suggests that s + 8 can be rational or irrational, depending on the value of s. However, since s is given as irrational, adding a rational number (8) to it will always result in an irrational number. Therefore, choice (C) is incorrect.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

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Q. The number

s

is irrrational. Which statement about

s - 8

is true? Choices:

\newline

(A)

s - 8

is rational.

\newline

(B)

s + 8

is irrational.

\newline

(C)

s + 8

can be rational or irrational, depending on the value of

s

Identify Number Type: Identify whether the number $8$ is a rational or irrational number. $8$ is a whole number, and all whole numbers are rational numbers.
Determine $s - 8$ : We know: $\newline$ $s$ is an irrational number. $\newline$ $8$ is a rational number. $\newline$ Which statement about $s - 8$ is true? $\newline$ Subtracting a rational number from an irrational number results in an irrational number.
Evaluate $s - 8$ : Therefore, $s - 8$ is irrational, which means that choice $(A)$ is incorrect.
Evaluate $s + 8$ : Since adding or subtracting a rational number from an irrational number always results in an irrational number, $s + 8$ is also irrational, which means that choice (B) is correct.
Evaluate $s + 8$ : Choice (C) suggests that $s + 8$ can be rational or irrational, depending on the value of $s$ . However, since $s$ is given as irrational, adding a rational number ( $8$ ) to it will always result in an irrational number. Therefore, choice (C) is incorrect.