Question
Which statement is true about the square root of 28? It is between 5 and 6, proably closer to 5. It is between 5 and 6, probably closer to 6. It is between 4 and 5, probably closer to 5. It is between 6 and 7, probably closer to 6.
Answers
Answer
Which statement is true about the integer fraction that equals the square root of 2? It is equal to 1. it invovles large numbers. It requires a computer to find it. It does not exist.
Answer
Identify which condition is necessary for a number to be rational. It must not be negative. It must be written as a fraction. It must be able to be expressed as an integer divided by a nonzero integer. It must not be an endless decimal.
Answered by
GPT-4o mini
To determine the location of the square root of 28, we can estimate its value by finding the squares of whole numbers around it.
The square of 5 is \(5^2 = 25\), and the square of 6 is \(6^2 = 36\). Since \(25 < 28 < 36\), we can conclude that \(5 < \sqrt{28} < 6\).
Next, we can compare \(28\) to the numbers closer to the squares of \(5.3\) and \(5.4\):
- \(5.3^2 = 28.09\)
- \(5.2^2 = 27.04\)
Since \(27.04 < 28 < 28.09\), \(\sqrt{28}\) is between \(5.2\) and \(5.3\).
Thus, \(\sqrt{28}\) is definitely between 5 and 6, but it is closer to 6 because it is closer to \(5.3\) rather than \(5.2\).
So, the correct statement is: **It is between 5 and 6, probably closer to 6.**
The square of 5 is \(5^2 = 25\), and the square of 6 is \(6^2 = 36\). Since \(25 < 28 < 36\), we can conclude that \(5 < \sqrt{28} < 6\).
Next, we can compare \(28\) to the numbers closer to the squares of \(5.3\) and \(5.4\):
- \(5.3^2 = 28.09\)
- \(5.2^2 = 27.04\)
Since \(27.04 < 28 < 28.09\), \(\sqrt{28}\) is between \(5.2\) and \(5.3\).
Thus, \(\sqrt{28}\) is definitely between 5 and 6, but it is closer to 6 because it is closer to \(5.3\) rather than \(5.2\).
So, the correct statement is: **It is between 5 and 6, probably closer to 6.**
Answered by
GPT-4o mini
The correct statement regarding the square root of 2 in the context of integer fractions is: **It does not exist.**
The square root of 2 is an irrational number, meaning it cannot be expressed as a fraction of two integers (i.e., it cannot be written as \( \frac{a}{b} \) where \( a \) and \( b \) are integers). It is approximately 1.41421356..., and its decimal representation goes on forever without repeating. Therefore, there is no integer fraction that equals the square root of 2.
The square root of 2 is an irrational number, meaning it cannot be expressed as a fraction of two integers (i.e., it cannot be written as \( \frac{a}{b} \) where \( a \) and \( b \) are integers). It is approximately 1.41421356..., and its decimal representation goes on forever without repeating. Therefore, there is no integer fraction that equals the square root of 2.
Answered by
GPT-4o mini
The necessary condition for a number to be rational is: **It must be able to be expressed as an integer divided by a nonzero integer.**
A rational number is defined as any number that can be expressed in the form \( \frac{a}{b} \), where \( a \) is an integer and \( b \) is a nonzero integer. This definition encompasses both fractions and integers, as any integer \( n \) can be expressed as \( \frac{n}{1} \).
The other options are not necessary conditions for a number to be rational:
- A rational number can be negative (e.g., \(-\frac{1}{2}\)).
- While rational numbers can be written as fractions, the key point is that they can be expressed in the form of an integer over a nonzero integer.
- Rational numbers can include endless decimals, but they will be repeating decimals (e.g., \(0.333...\) is rational because it can be expressed as \( \frac{1}{3} \)).
Thus, the third option is the correct description of a necessary condition for a number to be rational.
A rational number is defined as any number that can be expressed in the form \( \frac{a}{b} \), where \( a \) is an integer and \( b \) is a nonzero integer. This definition encompasses both fractions and integers, as any integer \( n \) can be expressed as \( \frac{n}{1} \).
The other options are not necessary conditions for a number to be rational:
- A rational number can be negative (e.g., \(-\frac{1}{2}\)).
- While rational numbers can be written as fractions, the key point is that they can be expressed in the form of an integer over a nonzero integer.
- Rational numbers can include endless decimals, but they will be repeating decimals (e.g., \(0.333...\) is rational because it can be expressed as \( \frac{1}{3} \)).
Thus, the third option is the correct description of a necessary condition for a number to be rational.
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