HELP PLEASE I NEED THIS DONE Rational and Irrational Numbers Quick Check
1. identify which condition is necessary for a number to be rational.(1 point)
Responses
It must not be negative.
It must be able to be expressed as an integer divided by a nonzero integer.
It must be written as a fraction.
It must not be an endless decimal.
2. Which of the following is irrational?(1 point)
Responses
3√4
−7 8/37
52.781654292
3.6363636363636363...
3.Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses
9.8
7.1
8.4
6.4
4. Which statement is true about the square root of 28?(1 point)
Responses
It is between 5 and 6, probably closer to 5.
It is between 4 and 5, probably closer to 5.
It is between 6 and 7, probably closer to 6.
It is between 5 and 6, probably closer to 6.
5. Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It requires a computer to find it.
It does not exist.
It involves large numbers.
It is equal to 1.
HELP ASAP @bot ANYONE PLS
1. The correct response is: It must be able to be expressed as an integer divided by a nonzero integer.
2. The correct response is: 3√4
3. The best estimate for 6×2–√ is 6.4.
4. The correct response is: It is between 5 and 6, probably closer to 6.
5. The correct response is: It does not exist.
Which of the following is irrational?(1 point)
Responses
√3/4
−7 8/37
52.781654292
3.6363636363636363...
The irrational number among the given options is:
√3/4
I can help with that! Here are the step-by-step answers to your questions:
1. The condition necessary for a number to be rational is that it must be able to be expressed as an integer divided by a nonzero integer.
2. To determine which of the given options is irrational, evaluate each one:
- 3√4: This is the cube root of 4, which is a rational number since 4 is a perfect cube.
- −7 8/37: This is a mixed number, which can be written as a fraction −(7*37 + 8)/37. This is a rational number.
- 52.781654292: This is a decimal number, but it is a terminating decimal, so it is a rational number.
- 3.6363636363636363...: This is a repeating decimal, which is an irrational number.
Therefore, the number 3.6363636363636363... is irrational.
3. To estimate the value of 6×2–√, perform the operations first:
6×2–√ = 6×2–√(2)
= 6×2–√(4)
= 12–2, since the square root of 4 is 2.
= 10
The best estimate for 6×2–√ is 10.
4. To determine the statement true about the square root of 28, we need to find an estimation:
The square root of 28 is between 5 and 6 because 5² = 25 and 6² = 36. It is closer to 5 than 6.
Therefore, the statement "It is between 5 and 6, probably closer to 5" is true about the square root of 28.
5. The square root of 2 cannot be expressed as an integer fraction. It is an irrational number.
Therefore, the statement "It does not exist" is true about the integer fraction that equals the square root of 2.
I hope this helps! Let me know if you have any further questions.
1. To identify the condition necessary for a number to be rational, we need to understand what rational numbers are. Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero.
Now, let's look at the given responses:
- It must not be negative: This condition is not necessary for a number to be rational. A rational number can be positive or negative.
- It must be able to be expressed as an integer divided by a nonzero integer: This is the correct condition for a number to be rational. It means that the number can be written as a fraction of two integers.
- It must be written as a fraction: While this is true for rational numbers, it is not the necessary condition. A rational number can also be expressed as a decimal.
- It must not be an endless decimal: This condition is not necessary for a number to be rational. A rational number can be terminating (finite) or repeating (infinite) decimal.
Therefore, the answer to the first question is: "It must be able to be expressed as an integer divided by a nonzero integer."
2. To identify which number is irrational, we need to understand what irrational numbers are. Irrational numbers are those that cannot be expressed as a fraction of two integers. They are non-repeating and non-terminating decimals.
Now, let's look at the given responses:
- 3√4: This is a rational number since it can be simplified to 2, which is an integer.
- −7 8/37: This is a rational number since it is written as a fraction.
- 52.781654292: This is a rational number since it is a finite decimal.
- 3.6363636363636363...: This is an irrational number since it is a repeating decimal.
Therefore, the answer to the second question is: "3.6363636363636363..."
3. To estimate the value of 6×2–√, we need to simplify the expression.
6×2–√ can be rewritten as 6×(2–√). To calculate this, we need to know the approximate value of √2. It is approximately 1.414.
Now, substituting the value of √2, we have:
6×(2–√) ≈ 6×(2–1.414) ≈ 6×0.586 ≈ 3.516.
Out of the given choices, the best estimate for 6×2–√ is 3.5, which is closest to 3.516.
Therefore, the answer to the third question is: "7.1"
4. To determine the true statement about the square root of 28, we need to find a reasonable estimate.
The square root of 28 is between 5 and 6 because 5² = 25 < 28 and 6² = 36 > 28.
Now, to determine which estimate is more reasonable, we can consider that 28 is closer to 25 than it is to 36. Therefore, the square root of 28 is probably closer to 5.
Therefore, the answer to the fourth question is: "It is between 5 and 6, probably closer to 5."
5. To determine the true statement about the integer fraction that equals the square root of 2, we need to understand what the square root of 2 is.
The square root of 2 is an irrational number and cannot be expressed as a fraction of two integers. However, if rounded to a whole number, it is equal to 1.
Therefore, the answer to the fifth question is: "It is equal to 1."
I hope this helps! Let me know if you have any further questions.