Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $s$ .

View step-by-step help

View step-by-step help

Properties of operations on rational and irrational numbers

Full solution

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.

More problems from Properties of operations on rational and irrational numbers

Question

t

is irrational. Which statement about

t - \sqrt{47}

\newline

\newline

t - \sqrt{47}

\newline

t - \sqrt{47}

\newline

t - \sqrt{47}

can be rational or irrational, depending on the value of

t

Posted 2 months ago

Question

(\frac{3}{14})\cdot(\frac{7}{71})

rational or irrational?

\newline

1

\newline

\newline

\newline

(C) It can be either rational or irrational

Posted 2 months ago

Question

Is the following number rational or irrational?

\newline

\frac{\pi}{5}

\newline

1

\newline

\newline

Posted 1 month ago

Question

Is the following number rational or irrational?

\newline

-3+\pi

\newline

1

\newline

\newline

Posted 2 months ago

Question

Is the following number rational or irrational?

\newline

-0.\overline{32}

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

\sqrt{121}

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

0.5555

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

7.11

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

\frac{0.3}{0.9}

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

-11\pi

\newline

1

\newline

\newline

Posted 2 months ago