Please answer all of these.
Identify which condition is necessary for a number to be rational.(1 point)
Responses
A. It must be written as a fraction.
b. It must be able to be expressed as an integer divided by a nonzero integer.
c. It must not be negative.
d. It must not be an endless decimal.
Which of the following is irrational?(1 point)
Responses
a. −7 8/37
b. 3.6363636363636363...
c. 3√/4
d. 52.781654292
Estimate the value of 6× the square root of 2. Which of the following choices is the best estimate?(1 point)
Responses
a. 6.4
b. 9.8
c. 7.1
d. 8.4
Which statement is true about the square root of 28?(1 point)
Responses
a. It is between 6 and 7, probably closer to 6.
b. It is between 5 and 6, probably closer to 6.
c. It is between 5 and 6, probably closer to 5.
d. It is between 4 and 5, probably closer to 5.
Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
a. It requires a computer to find it.
b. It does not exist.
c. It is equal to 1.
d. It involves large numbers.
please double check the answer
B. It is between 5 and 6, probably closer to 5.
everything else 100%
1. The necessary condition for a number to be rational is: b. It must be able to be expressed as an integer divided by a nonzero integer.
2. The irrational number among the options is: b. 3.6363636363636363...
3. The best estimate for 6 times the square root of 2 is: d. 8.4
4. The true statement about the square root of 28 is: a. It is between 6 and 7, probably closer to 6.
5. The true statement about the integer fraction that equals the square root of 2 is: b. It does not exist.
To answer these questions:
1. In order for a number to be rational, it must be able to be expressed as an integer divided by a nonzero integer. Therefore, the correct answer is B. To identify this, you need to know the definition of a rational number and understand that it can be written as a fraction.
2. To determine which of the given options is irrational, you need to understand that an irrational number cannot be expressed as a fraction or a repeating or terminating decimal. Looking at the options, the only one that fits this criteria is option B, which is 3.6363636363636363... This repeating decimal indicates that the number is non-terminating and non-repeating.
3. To estimate the value of 6 times the square root of 2, you need to know the approximate value of the square root of 2. The square root of 2 is approximately 1.414. Multiplying this by 6 gives an estimate of approximately 8.484. The closest option to this estimate is D, 8.4.
4. To determine the statement that is true about the square root of 28, you need to know its value. The square root of 28 is between 5 and 6. Since 28 is closer to 25 (5 squared) than it is to 36 (6 squared), the square root of 28 is closer to 5. Therefore, the correct answer is B. It is between 5 and 6, probably closer to 6.
5. To determine the statement that is true about the integer fraction that equals the square root of 2, you need to understand that the square root of 2 cannot be expressed as a fraction. Therefore, the correct answer is B. It does not exist. This can be determined through mathematical proofs that show the irrationality of the square root of 2.
1. The condition that is necessary for a number to be rational is:
B. It must be able to be expressed as an integer divided by a nonzero integer.
2. The irrational number among the given options is:
C. 3√/4
3. The best estimate for 6 times the square root of 2 is:
D. 8.4
4. The statement that is true about the square root of 28 is:
B. It is between 5 and 6, probably closer to 6.
5. The statement that is true about the integer fraction that equals the square root of 2 is:
B. It does not exist.
Upon reviewing the responses, there is an error in the second question. The correct answer is:
b. 3.6363636363636363...
I apologize for the mistake. Thank you for bringing it to my attention.