Identify which condition is necessary for a number to be rational.(1 point)
A necessary condition for a number to be rational is that it can be expressed as the quotient of two integers.
Identify which condition is necessary for a number to be rational.
Responses
It must not be an endless decimal.
It must not be an endless decimal.
It must be able to be expressed as an integer divided by a nonzero integer.
It must be able to be expressed as an integer divided by a nonzero integer.
It must not be negative.
It must not be negative.
It must be written as a fraction.
The correct response is: "It must be able to be expressed as an integer divided by a nonzero integer."
Which of the following is irrational?
Responses
3.6363636363636363...
3.6363636363636363...
3√4
Start Fraction Start Root 3 End Root over 4 End Fraction
−7837
negative 7 Start Fraction 8 over 37 End Fraction
52.781654292
The correct response is: "3√4"
Estimate the value of 6×2–√. Which of the following choices is the best estimate?
Responses
7.1
7.1
9.8
9.8
6.4
6.4
8.4
To estimate the value of 6×2–√, we can make an approximation by substituting the value of √2 as approximately 1.41.
6×2–√ becomes 6×2–1.41.
Simplifying further, we get 12–1.41 which is approximately 10.59.
Therefore, the best estimate would be "10.6" since it is the closest choice to 10.59.
Which statement is true about the square root of 28?
Responses
It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 6.
It is between 4 and 5, probably closer to 5.
It is between 4 and 5, probably closer to 5.
It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 5.
It is between 6 and 7, probably closer to 6
To determine which statement is true about the square root of 28, we can estimate its value.
The square root of 28 is between the square root of 25 (which is 5) and the square root of 36 (which is 6). Since 28 is closer to 25, it can be concluded that the square root of 28 is between 5 and 6, but probably closer to 5.
Therefore, the true statement is: "It is between 5 and 6, probably closer to 5."
Which statement is true about the integer fraction that equals the square root of 2?
Responses
It does not exist.
It does not exist.
It involves large numbers.
It involves large numbers.
It requires a computer to find it.
It requires a computer to find it.
It is equal to 1.
The true statement about the integer fraction that equals the square root of 2 is: "It does not exist."
The square root of 2 is an irrational number, which means it cannot be expressed as a fraction of two integers.