Asked by UnicornSparkles
what is the definition of an irrational number
A: a number that can be written as a fraction but not as a decimal
B: a negative number
C: a number that can be expressed as a fraction p/q where p and q are integers and q is not equal to zero
D: a number that cannot be expressed as a fraction p/q where p and q are integers and q is not equal to zero
A: a number that can be written as a fraction but not as a decimal
B: a negative number
C: a number that can be expressed as a fraction p/q where p and q are integers and q is not equal to zero
D: a number that cannot be expressed as a fraction p/q where p and q are integers and q is not equal to zero
Answers
Answered by
UnicornSparkles
which of the following best describes the number shown below?
square root of 2
A: rational
B: irrational
C: neither rational nor irrational
D: both rational and irrational
square root of 2
A: rational
B: irrational
C: neither rational nor irrational
D: both rational and irrational
Answered by
UnicornSparkles
which of the following is a irrational number?
A: square root of 36
B: 3/5
C: 3.8
D: square root of 18
A: square root of 36
B: 3/5
C: 3.8
D: square root of 18
Answered by
UnicornSparkles
which number is most likely an irrational number?
A: -1.500000000
B: -9.121212121
C: -7.855555555
D: -5.690134489
A: -1.500000000
B: -9.121212121
C: -7.855555555
D: -5.690134489
Answered by
UnicornSparkles
Which statement correctly describes the number square root of 22 = 4.690415
A: The number is rational because is can be written as a non-repeating, non-terminating decimal
B: The number is rational because it can be written as a terminating decimal
C: The number is irrational because it can be written as a terminating decimal
D: The number is irrational because it can be written as a non-repeating, non-terminating decimal
A: The number is rational because is can be written as a non-repeating, non-terminating decimal
B: The number is rational because it can be written as a terminating decimal
C: The number is irrational because it can be written as a terminating decimal
D: The number is irrational because it can be written as a non-repeating, non-terminating decimal
Answered by
UnicornSparkles
(select all the correct answers)
Which numbers are irrational
A: -6.398572639
B: 3/11 = 0. line over 27
C: 2(pi)/4 = 1.570796…
D: square root of 16 = 4
E: square root of 8 = 2.82842712
F: -15/16 = -0.9375
Which numbers are irrational
A: -6.398572639
B: 3/11 = 0. line over 27
C: 2(pi)/4 = 1.570796…
D: square root of 16 = 4
E: square root of 8 = 2.82842712
F: -15/16 = -0.9375
Answered by
UnicornSparkles
(select all the correct answers)
Which numbers are irrational
A: square root of 6/3 = 0.81649658…
B: -15/16 = -0.8333 line over 3
C: -3.857634857
D: square root of 36/14 0. line over 428571
E: 8/2(pi) = 12.5663706
F: -18.493847583
Which numbers are irrational
A: square root of 6/3 = 0.81649658…
B: -15/16 = -0.8333 line over 3
C: -3.857634857
D: square root of 36/14 0. line over 428571
E: 8/2(pi) = 12.5663706
F: -18.493847583
Answered by
UnicornSparkles
E and what? or is it just E
Answered by
UnicornSparkles
which of the following is a rational number
A: pi
B: square root of 121
C: square root of 51
D: square root of 21
A: pi
B: square root of 121
C: square root of 51
D: square root of 21
Answered by
GPT-4o mini
The correct definition of an irrational number is:
**D: a number that cannot be expressed as a fraction p/q where p and q are integers and q is not equal to zero.**
Irrational numbers cannot be represented as simple fractions and their decimal expansions are non-repeating and non-terminating. Examples include numbers like \( \sqrt{2} \) and \( \pi \).
**D: a number that cannot be expressed as a fraction p/q where p and q are integers and q is not equal to zero.**
Irrational numbers cannot be represented as simple fractions and their decimal expansions are non-repeating and non-terminating. Examples include numbers like \( \sqrt{2} \) and \( \pi \).
Answered by
GPT-4o mini
The correct description of the number \( \sqrt{2} \) is:
**B: irrational.**
The square root of 2 cannot be expressed as a fraction \( p/q \) where \( p \) and \( q \) are integers, making it an irrational number.
**B: irrational.**
The square root of 2 cannot be expressed as a fraction \( p/q \) where \( p \) and \( q \) are integers, making it an irrational number.
Answered by
GPT-4o mini
The number that is irrational among the options given is:
**D: square root of 18.**
The square root of 18 can be simplified to \( 3\sqrt{2} \), which is not a whole number and cannot be expressed as a fraction of integers, making it irrational.
- **A: square root of 36** is rational since it equals 6.
- **B: 3/5** is a rational number.
- **C: 3.8** is also a rational number since it can be expressed as a fraction (e.g., \( 38/10 \)).
**D: square root of 18.**
The square root of 18 can be simplified to \( 3\sqrt{2} \), which is not a whole number and cannot be expressed as a fraction of integers, making it irrational.
- **A: square root of 36** is rational since it equals 6.
- **B: 3/5** is a rational number.
- **C: 3.8** is also a rational number since it can be expressed as a fraction (e.g., \( 38/10 \)).
Answered by
GPT-4o mini
Among the options given, the number that is most likely to be irrational is:
**D: -5.690134489.**
This number appears to be a decimal that does not terminate or repeat visibly. However, without specific context about its decimal representation (whether it continues indefinitely or has a repeating pattern), it could still theoretically be rational if it is a finite decimal.
In contrast:
- **A: -1.500000000** is rational (it can be expressed as \(-3/2\)).
- **B: -9.121212121** is rational (it has a repeating decimal .12).
- **C: -7.855555555** is also rational (it has a repeating decimal .555).
Thus, **D** is the best candidate for being irrational, but please note that without additional context about the nature of the decimal, it's based on its presentation rather than a definitive classification.
**D: -5.690134489.**
This number appears to be a decimal that does not terminate or repeat visibly. However, without specific context about its decimal representation (whether it continues indefinitely or has a repeating pattern), it could still theoretically be rational if it is a finite decimal.
In contrast:
- **A: -1.500000000** is rational (it can be expressed as \(-3/2\)).
- **B: -9.121212121** is rational (it has a repeating decimal .12).
- **C: -7.855555555** is also rational (it has a repeating decimal .555).
Thus, **D** is the best candidate for being irrational, but please note that without additional context about the nature of the decimal, it's based on its presentation rather than a definitive classification.
Answered by
GPT-4o mini
The correct statement that describes the number \( \sqrt{22} \approx 4.690415 \) is:
**D: The number is irrational because it can be written as a non-repeating, non-terminating decimal.**
The square root of 22 is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal form is non-repeating and non-terminating, which is characteristic of irrational numbers.
**D: The number is irrational because it can be written as a non-repeating, non-terminating decimal.**
The square root of 22 is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal form is non-repeating and non-terminating, which is characteristic of irrational numbers.
Answered by
GPT-4o mini
The correct answers for which numbers are irrational are:
**B: \( \frac{3}{11} = 0.\overline{27} \)** - This is a repeating decimal, and hence it is rational, not irrational.
**C: \( \frac{2\pi}{4} = 1.570796… \)** - This is \( \frac{\pi}{2} \), which is irrational because \( \pi \) is an irrational number and any multiple of an irrational number is also irrational.
**E: \( \sqrt{8} = 2.82842712 \)** - This is an irrational number. It cannot be expressed as a fraction of two integers.
**A: -6.398572639** and **F: -\frac{15}{16} = -0.9375** are rational numbers because they can be expressed as fractions (the latter is a terminating decimal).
**D: \( \sqrt{16} = 4 \)** is also a rational number since it is an integer.
So, the correct selections are:
- **C** (because it involves π which is irrational)
- **E** (because \(\sqrt{8}\) is not a perfect square and thus irrational).
**B: \( \frac{3}{11} = 0.\overline{27} \)** - This is a repeating decimal, and hence it is rational, not irrational.
**C: \( \frac{2\pi}{4} = 1.570796… \)** - This is \( \frac{\pi}{2} \), which is irrational because \( \pi \) is an irrational number and any multiple of an irrational number is also irrational.
**E: \( \sqrt{8} = 2.82842712 \)** - This is an irrational number. It cannot be expressed as a fraction of two integers.
**A: -6.398572639** and **F: -\frac{15}{16} = -0.9375** are rational numbers because they can be expressed as fractions (the latter is a terminating decimal).
**D: \( \sqrt{16} = 4 \)** is also a rational number since it is an integer.
So, the correct selections are:
- **C** (because it involves π which is irrational)
- **E** (because \(\sqrt{8}\) is not a perfect square and thus irrational).
Answered by
GPT-4o mini
To determine which of the given options are irrational numbers, let's analyze each one:
**A: \( \sqrt{6}/3 \approx 0.81649658…**
- This value is a non-terminating decimal and since \( \sqrt{6} \) is an irrational number, dividing it by a rational number (3) does not change its irrationality. Therefore, this is **irrational**.
**B: \(-15/16 = -0.8333\overline{3}**
- This is a repeating decimal and can be expressed as a fraction. Thus, it is **rational**.
**C: \(-3.857634857**
- This is a terminating decimal, so it can be expressed as a fraction. Thus, it is **rational**.
**D: \( \sqrt{36}/14 = 6/14 = 3/7 \) (This part seems incorrectly interpreted as a decimal conversion; however, if we consider \( \sqrt{36}\) directly, it is rational.)**
- \(\sqrt{36}\) is 6, a rational number. This would thus imply that the representation provided here does not hold and leads to confusion.
**E: \( \frac{8}{2\pi} = 4/\pi \approx 1.273239 \) (as a value) is irrational.**
- Since \(\pi\) is irrational, any fraction involving it also is, thus this is **irrational**.
**F: \(-18.493847583**
- This is a terminating decimal, so it can be expressed as a fraction. Thus, it is **rational**.
### Summary of Irrational Numbers:
- **A: \( \sqrt{6}/3 \)** (irrational)
- **E: \( \frac{8}{2\pi} \)** (irrational)
### Correct Selections:
- **A**
- **E**
**A: \( \sqrt{6}/3 \approx 0.81649658…**
- This value is a non-terminating decimal and since \( \sqrt{6} \) is an irrational number, dividing it by a rational number (3) does not change its irrationality. Therefore, this is **irrational**.
**B: \(-15/16 = -0.8333\overline{3}**
- This is a repeating decimal and can be expressed as a fraction. Thus, it is **rational**.
**C: \(-3.857634857**
- This is a terminating decimal, so it can be expressed as a fraction. Thus, it is **rational**.
**D: \( \sqrt{36}/14 = 6/14 = 3/7 \) (This part seems incorrectly interpreted as a decimal conversion; however, if we consider \( \sqrt{36}\) directly, it is rational.)**
- \(\sqrt{36}\) is 6, a rational number. This would thus imply that the representation provided here does not hold and leads to confusion.
**E: \( \frac{8}{2\pi} = 4/\pi \approx 1.273239 \) (as a value) is irrational.**
- Since \(\pi\) is irrational, any fraction involving it also is, thus this is **irrational**.
**F: \(-18.493847583**
- This is a terminating decimal, so it can be expressed as a fraction. Thus, it is **rational**.
### Summary of Irrational Numbers:
- **A: \( \sqrt{6}/3 \)** (irrational)
- **E: \( \frac{8}{2\pi} \)** (irrational)
### Correct Selections:
- **A**
- **E**
Answered by
GPT-4o mini
The only options that are irrational from the list you provided are:
- **A: \( \sqrt{6}/3 \)** (irrational)
- **E: \( \frac{8}{2\pi} \)** (irrational)
So the correct selections are **A** and **E**.
- **A: \( \sqrt{6}/3 \)** (irrational)
- **E: \( \frac{8}{2\pi} \)** (irrational)
So the correct selections are **A** and **E**.
Answered by
GPT-4o mini
The number that is a rational number among the options given is:
**B: square root of 121.**
This simplifies to \(11\), which is a whole number and can be expressed as a fraction \(\frac{11}{1}\).
The other options are:
- **A: pi (\(\pi\))** is an irrational number.
- **C: square root of 51** is irrational.
- **D: square root of 21** is also irrational.
So, the only rational number in the list is **B**.
**B: square root of 121.**
This simplifies to \(11\), which is a whole number and can be expressed as a fraction \(\frac{11}{1}\).
The other options are:
- **A: pi (\(\pi\))** is an irrational number.
- **C: square root of 51** is irrational.
- **D: square root of 21** is also irrational.
So, the only rational number in the list is **B**.
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