QuestionIdentify the option that is not a rational number: $0.\overline{65}$ , $\sqrt{2.739}$ , 6.775, $\sqrt{0.0625}$ .

Studdy Solution

STEP 1

Assumptions1. A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. . The decimal representation of a rational number either ends (terminates) after a finite number of digits or begins to repeat the same finite sequence of digits over and over (repeats).
3. A number that cannot be expressed as a ratio of two integers is an irrational number.

STEP 2

Let's analyze each option separately.
First, consider the number $0 . \overline{65}$ . This is a repeating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

STEP 3

Next, consider the number $\sqrt{2.739}$ . To determine if this is a rational number, we need to find its square root. If the square root is a rational number, then $\sqrt{2.739}$ is a rational number. If the square root is not a rational number, then $\sqrt{2.739}$ is not a rational number.

STEP 4

Calculate the square root of $2.739$ .
$\sqrt{2.739} \approx1.65529$

STEP 5

The square root of $2.739$ is a non-repeating, non-terminating decimal, which means it cannot be expressed as a ratio of two integers. Therefore, $\sqrt{2.739}$ is not a rational number.

STEP 6

Next, consider the number $6.775$ . This is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

STEP 7

Finally, consider the number $\sqrt{0.0625}$ . To determine if this is a rational number, we need to find its square root. If the square root is a rational number, then $\sqrt{0.0625}$ is a rational number. If the square root is not a rational number, then $\sqrt{0.0625}$ is not a rational number.

STEP 8

Calculate the square root of $0.0625$ .
$\sqrt{0.0625} =0.25$

STEP 9

The square root of $.0625$ is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, $\sqrt{.0625}$ is a rational number.

STEP 10

After analyzing all the options, we can conclude that the number $\sqrt{2.739}$ is not a rational number.
The solution is $\sqrt{2.739}$ .

Was this helpful?

QuestionIdentify the option that is not a rational number: $0.\overline{65}$ , $\sqrt{2.739}$ , 6.775, $\sqrt{0.0625}$ .

Studdy Solution

STEP 1

STEP 2

Let's analyze each option separately.
First, consider the number $0 . \overline{65}$ . This is a repeating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

STEP 3

Next, consider the number $\sqrt{2.739}$ . To determine if this is a rational number, we need to find its square root. If the square root is a rational number, then $\sqrt{2.739}$ is a rational number. If the square root is not a rational number, then $\sqrt{2.739}$ is not a rational number.

STEP 4

Calculate the square root of $2.739$ .
$\sqrt{2.739} \approx1.65529$

STEP 5

The square root of $2.739$ is a non-repeating, non-terminating decimal, which means it cannot be expressed as a ratio of two integers. Therefore, $\sqrt{2.739}$ is not a rational number.

STEP 6

Next, consider the number $6.775$ . This is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

STEP 7

Finally, consider the number $\sqrt{0.0625}$ . To determine if this is a rational number, we need to find its square root. If the square root is a rational number, then $\sqrt{0.0625}$ is a rational number. If the square root is not a rational number, then $\sqrt{0.0625}$ is not a rational number.

STEP 8

Calculate the square root of $0.0625$ .
$\sqrt{0.0625} =0.25$

STEP 9

The square root of $.0625$ is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, $\sqrt{.0625}$ is a rational number.

STEP 10

After analyzing all the options, we can conclude that the number $\sqrt{2.739}$ is not a rational number.
The solution is $\sqrt{2.739}$ .

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionIdentify the option that is not a rational number: 0.65‾0.\overline{65}0.65, 2.739\sqrt{2.739}2.739​, 6.775, 0.0625\sqrt{0.0625}0.0625​.

Studdy Solution

STEP 1

STEP 2

Let's analyze each option separately.First, consider the number 0.65‾0 . \overline{65}0.65. This is a repeating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

STEP 3

STEP 4

Calculate the square root of 2.7392.7392.739.2.739≈1.65529\sqrt{2.739} \approx1.655292.739​≈1.65529

STEP 5

The square root of 2.7392.7392.739 is a non-repeating, non-terminating decimal, which means it cannot be expressed as a ratio of two integers. Therefore, 2.739\sqrt{2.739}2.739​ is not a rational number.

STEP 6

Next, consider the number 6.7756.7756.775. This is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

STEP 7

STEP 8

Calculate the square root of 0.06250.06250.0625.0.0625=0.25\sqrt{0.0625} =0.250.0625​=0.25

STEP 9

The square root of .0625.0625.0625 is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, .0625\sqrt{.0625}.0625​ is a rational number.

STEP 10

After analyzing all the options, we can conclude that the number 2.739\sqrt{2.739}2.739​ is not a rational number.The solution is 2.739\sqrt{2.739}2.739​.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionIdentify the option that is not a rational number: $0.\overline{65}$ , $\sqrt{2.739}$ , 6.775, $\sqrt{0.0625}$ .

Let's analyze each option separately.
First, consider the number $0 . \overline{65}$ . This is a repeating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

Calculate the square root of $2.739$ .
$\sqrt{2.739} \approx1.65529$

The square root of $2.739$ is a non-repeating, non-terminating decimal, which means it cannot be expressed as a ratio of two integers. Therefore, $\sqrt{2.739}$ is not a rational number.

Next, consider the number $6.775$ . This is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, it is a rational number.

Calculate the square root of $0.0625$ .
$\sqrt{0.0625} =0.25$

The square root of $.0625$ is a terminating decimal, which means it can be expressed as a ratio of two integers. Therefore, $\sqrt{.0625}$ is a rational number.

After analyzing all the options, we can conclude that the number $\sqrt{2.739}$ is not a rational number.
The solution is $\sqrt{2.739}$ .