Solved on Oct 30, 2023

Determine which statements are true: $\sqrt{4}$ is rational and integer, $\sqrt{3}$ is rational, 0 is neither rational nor irrational, $-6.1\overline{33}$ is irrational.

STEP 1

Assumptions1. A rational number can be expressed as a fraction where both the numerator and denominator are integers and the denominator is not zero. . An integer is a whole number that can be positive, negative, or zero.
3. An irrational number cannot be expressed as a fraction and its decimal representation never ends or repeats.

STEP 2

Let's evaluate each statement one by one. Starting with the first statement, $\sqrt{4}$ is a rational number and an integer.

STEP 3

Calculate the square root of.
$\sqrt{} =2$

STEP 4

Since2 can be expressed as a fraction (2/1) and is a whole number, it is both a rational number and an integer. Therefore, the first statement is true.

STEP 5

Now, let's evaluate the second statement, $\sqrt{3}$ is a rational number.

STEP 6

Calculate the square root of3.
$\sqrt{3} \approx1.73205$

STEP 7

Since the decimal representation of $\sqrt{3}$ never ends or repeats, it cannot be expressed as a fraction. Therefore, $\sqrt{3}$ is not a rational number. The second statement is false.

STEP 8

Next, let's evaluate the third statement,0 is neither a rational number nor an irrational number.

STEP 9

Zero can be expressed as a fraction where the numerator is zero and the denominator is any non-zero integer. Therefore, is a rational number. The third statement is false.

STEP 10

Finally, let's evaluate the fourth statement, $-6. \overline{33}$ is an irrational number.

STEP 11

The number $-6. \overline{33}$ is a repeating decimal, which means it can be expressed as a fraction. Therefore, $-6. \overline{33}$ is a rational number, not an irrational number. The fourth statement is false.
Therefore, the only true statement is $\sqrt{4}$ is a rational number and an integer.

Was this helpful?

Determine which statements are true: $\sqrt{4}$ is rational and integer, $\sqrt{3}$ is rational, 0 is neither rational nor irrational, $-6.1\overline{33}$ is irrational.

STEP 1

STEP 2

Let's evaluate each statement one by one. Starting with the first statement, $\sqrt{4}$ is a rational number and an integer.

STEP 3

Calculate the square root of.
$\sqrt{} =2$

STEP 4

Since2 can be expressed as a fraction (2/1) and is a whole number, it is both a rational number and an integer. Therefore, the first statement is true.

STEP 5

Now, let's evaluate the second statement, $\sqrt{3}$ is a rational number.

STEP 6

Calculate the square root of3.
$\sqrt{3} \approx1.73205$

STEP 7

Since the decimal representation of $\sqrt{3}$ never ends or repeats, it cannot be expressed as a fraction. Therefore, $\sqrt{3}$ is not a rational number. The second statement is false.

STEP 8

Next, let's evaluate the third statement,0 is neither a rational number nor an irrational number.

STEP 9

Zero can be expressed as a fraction where the numerator is zero and the denominator is any non-zero integer. Therefore, is a rational number. The third statement is false.

STEP 10

Finally, let's evaluate the fourth statement, $-6. \overline{33}$ is an irrational number.

STEP 11

The number $-6. \overline{33}$ is a repeating decimal, which means it can be expressed as a fraction. Therefore, $-6. \overline{33}$ is a rational number, not an irrational number. The fourth statement is false.
Therefore, the only true statement is $\sqrt{4}$ is a rational number and an integer.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine which statements are true: 4\sqrt{4}4​ is rational and integer, 3\sqrt{3}3​ is rational, 0 is neither rational nor irrational, −6.133‾-6.1\overline{33}−6.133 is irrational.

STEP 1

STEP 2

Let's evaluate each statement one by one. Starting with the first statement, 4\sqrt{4}4​ is a rational number and an integer.

STEP 3

Calculate the square root of.=2\sqrt{} =2​=2

STEP 4

Since2 can be expressed as a fraction (2/1) and is a whole number, it is both a rational number and an integer. Therefore, the first statement is true.

STEP 5

Now, let's evaluate the second statement, 3\sqrt{3}3​ is a rational number.

STEP 6

Calculate the square root of3.3≈1.73205\sqrt{3} \approx1.732053​≈1.73205

STEP 7

Since the decimal representation of 3\sqrt{3}3​ never ends or repeats, it cannot be expressed as a fraction. Therefore, 3\sqrt{3}3​ is not a rational number. The second statement is false.

STEP 8

Next, let's evaluate the third statement,0 is neither a rational number nor an irrational number.

STEP 9

Zero can be expressed as a fraction where the numerator is zero and the denominator is any non-zero integer. Therefore, is a rational number. The third statement is false.

STEP 10

Finally, let's evaluate the fourth statement, −6.33‾-6. \overline{33}−6.33 is an irrational number.

STEP 11

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine which statements are true: $\sqrt{4}$ is rational and integer, $\sqrt{3}$ is rational, 0 is neither rational nor irrational, $-6.1\overline{33}$ is irrational.

Let's evaluate each statement one by one. Starting with the first statement, $\sqrt{4}$ is a rational number and an integer.

Calculate the square root of.
$\sqrt{} =2$

Now, let's evaluate the second statement, $\sqrt{3}$ is a rational number.

Calculate the square root of3.
$\sqrt{3} \approx1.73205$

Since the decimal representation of $\sqrt{3}$ never ends or repeats, it cannot be expressed as a fraction. Therefore, $\sqrt{3}$ is not a rational number. The second statement is false.

Finally, let's evaluate the fourth statement, $-6. \overline{33}$ is an irrational number.