Question
which of these are rational number -1 12/27 , 22/3 , pi , 99
Answers
Answer
is sqrt 49 a real number
Answer
which of the following are integer
26/31 , 8.231 , sqrt19 , 82
26/31 , 8.231 , sqrt19 , 82
Answer
what is sqrt 16
whole number , integer, irrational number, natural number,
whole number , integer, irrational number, natural number,
Answer
which of the following is are irrational numbers
sqrt30, sqrt25, 33/89 , 99.8
sqrt30, sqrt25, 33/89 , 99.8
Answer
which of the following describes sqrt 172
real number
integer
rational number
irrational number
real number
integer
rational number
irrational number
Answered by
GPT-4o mini
A rational number is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).
Let's evaluate the numbers you provided:
1. **-1**: This can be expressed as \( \frac{-1}{1} \), so it is a rational number.
2. **12/27**: This is already in the form of a fraction \( \frac{12}{27} \), so it is a rational number.
3. **22/3**: This is also in the form of a fraction \( \frac{22}{3} \), so it is a rational number.
4. **π (pi)**: This is an irrational number, meaning it cannot be expressed as a fraction of two integers.
5. **99**: This can be expressed as \( \frac{99}{1} \), so it is a rational number.
So, the rational numbers from your list are: -1, 12/27, 22/3, and 99.
Let's evaluate the numbers you provided:
1. **-1**: This can be expressed as \( \frac{-1}{1} \), so it is a rational number.
2. **12/27**: This is already in the form of a fraction \( \frac{12}{27} \), so it is a rational number.
3. **22/3**: This is also in the form of a fraction \( \frac{22}{3} \), so it is a rational number.
4. **π (pi)**: This is an irrational number, meaning it cannot be expressed as a fraction of two integers.
5. **99**: This can be expressed as \( \frac{99}{1} \), so it is a rational number.
So, the rational numbers from your list are: -1, 12/27, 22/3, and 99.
Answered by
GPT-4o mini
Yes, \( \sqrt{49} \) is a real number. The square root of 49 is 7, since \( 7 \times 7 = 49 \). Therefore, \( \sqrt{49} = 7 \), which is indeed a real number.
In general, the square root of any non-negative number is a real number.
In general, the square root of any non-negative number is a real number.
Answered by
GPT-4o mini
An integer is a whole number that can be positive, negative, or zero, but it does not include fractions or decimals.
Let's evaluate the numbers you provided:
1. **26/31**: This is a fraction and not a whole number, so it is not an integer.
2. **8.231**: This is a decimal and not a whole number, so it is not an integer.
3. **√19**: The square root of 19 is an irrational number and not a whole number, so it is not an integer.
4. **82**: This is a whole number, so it is an integer.
So, from your list, the only integer is **82**.
Let's evaluate the numbers you provided:
1. **26/31**: This is a fraction and not a whole number, so it is not an integer.
2. **8.231**: This is a decimal and not a whole number, so it is not an integer.
3. **√19**: The square root of 19 is an irrational number and not a whole number, so it is not an integer.
4. **82**: This is a whole number, so it is an integer.
So, from your list, the only integer is **82**.
Answered by
GPT-4o mini
The square root of 16 is \( \sqrt{16} = 4 \).
Now let's categorize 4:
1. **Whole Number**: Yes, 4 is a whole number (whole numbers are non-negative integers, which include 0 and positive integers).
2. **Integer**: Yes, 4 is an integer (integers include all whole numbers and their negative counterparts).
3. **Irrational Number**: No, 4 is not an irrational number; it is a rational number because it can be expressed as \( \frac{4}{1} \).
4. **Natural Number**: Yes, 4 is a natural number (natural numbers are the set of positive integers: 1, 2, 3, ...).
In summary, \( \sqrt{16} = 4 \) is a whole number, an integer, and a natural number, but it is not an irrational number.
Now let's categorize 4:
1. **Whole Number**: Yes, 4 is a whole number (whole numbers are non-negative integers, which include 0 and positive integers).
2. **Integer**: Yes, 4 is an integer (integers include all whole numbers and their negative counterparts).
3. **Irrational Number**: No, 4 is not an irrational number; it is a rational number because it can be expressed as \( \frac{4}{1} \).
4. **Natural Number**: Yes, 4 is a natural number (natural numbers are the set of positive integers: 1, 2, 3, ...).
In summary, \( \sqrt{16} = 4 \) is a whole number, an integer, and a natural number, but it is not an irrational number.
Answered by
GPT-4o mini
To identify which of the numbers you provided are irrational, let's evaluate each one:
1. **\(\sqrt{30}\)**: This is an irrational number because 30 is not a perfect square, so \(\sqrt{30}\) cannot be expressed as a simple fraction or finite decimal.
2. **\(\sqrt{25}\)**: This is a rational number since \(\sqrt{25} = 5\), which is an integer.
3. **\(33/89\)**: This is a rational number because it is expressed as a fraction of two integers (33 and 89).
4. **\(99.8\)**: This is a rational number as well because it can be expressed as a fraction (\(99.8 = \frac{998}{10}\)), which is made up of integers.
### Summary:
The only irrational number from your list is **\(\sqrt{30}\)**. The others ( \(\sqrt{25}\), \(33/89\), and \(99.8\)) are all rational numbers.
1. **\(\sqrt{30}\)**: This is an irrational number because 30 is not a perfect square, so \(\sqrt{30}\) cannot be expressed as a simple fraction or finite decimal.
2. **\(\sqrt{25}\)**: This is a rational number since \(\sqrt{25} = 5\), which is an integer.
3. **\(33/89\)**: This is a rational number because it is expressed as a fraction of two integers (33 and 89).
4. **\(99.8\)**: This is a rational number as well because it can be expressed as a fraction (\(99.8 = \frac{998}{10}\)), which is made up of integers.
### Summary:
The only irrational number from your list is **\(\sqrt{30}\)**. The others ( \(\sqrt{25}\), \(33/89\), and \(99.8\)) are all rational numbers.
Answered by
GPT-4o mini
To classify \( \sqrt{172} \), let's evaluate its characteristics:
1. **Real Number**: Yes, \( \sqrt{172} \) is a real number since all square roots of non-negative numbers are real numbers.
2. **Integer**: No, \( \sqrt{172} \) is not an integer because it does not evaluate to a whole number (it is approximately \( 13.12 \)).
3. **Rational Number**: No, \( \sqrt{172} \) is not a rational number. A rational number can be expressed as a fraction of two integers; since 172 is not a perfect square, its square root cannot be expressed as a simple fraction and is not a terminating or repeating decimal.
4. **Irrational Number**: Yes, \( \sqrt{172} \) is an irrational number because it cannot be expressed as a fraction of two integers and its decimal representation is non-repeating and non-terminating.
### Summary:
- **Real Number**: Yes
- **Integer**: No
- **Rational Number**: No
- **Irrational Number**: Yes
Thus, \( \sqrt{172} \) is a **real number** and an **irrational number**.
1. **Real Number**: Yes, \( \sqrt{172} \) is a real number since all square roots of non-negative numbers are real numbers.
2. **Integer**: No, \( \sqrt{172} \) is not an integer because it does not evaluate to a whole number (it is approximately \( 13.12 \)).
3. **Rational Number**: No, \( \sqrt{172} \) is not a rational number. A rational number can be expressed as a fraction of two integers; since 172 is not a perfect square, its square root cannot be expressed as a simple fraction and is not a terminating or repeating decimal.
4. **Irrational Number**: Yes, \( \sqrt{172} \) is an irrational number because it cannot be expressed as a fraction of two integers and its decimal representation is non-repeating and non-terminating.
### Summary:
- **Real Number**: Yes
- **Integer**: No
- **Rational Number**: No
- **Irrational Number**: Yes
Thus, \( \sqrt{172} \) is a **real number** and an **irrational number**.
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