Identify which condition is necessary for a number to be rational.(1 point)
Responses
It must not be negative.
It must not be negative.
It must be written as a fraction.
It must be written as a fraction.
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 an endless decimal.
It must be able to be expressed as an integer divided by a nonzero integer.
Which of the following is irrational?(1 point)
Responses
52.781654292
52.781654292
3√4
Start Fraction Start Root 3 End Root over 4 End Fraction
3.6363636363636363...
3.6363636363636363...
−7837
3√4 (Start Fraction Start Root 3 End Root over 4 End Fraction)
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses
7.1
7.1
8.4
8.4
6.4
6.4
9.8
The best estimate for 6×2–√ is 6.4.
Which statement is true about the square root of 28?(1 point)
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
The statement "It is between 5 and 6, probably closer to 6" is true about the square root of 28.
Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It is equal to 1.
It is equal to 1.
It involves large numbers.
It involves large numbers.
It does not exist.
It does not exist.
It requires a computer to find it.
It requires a computer to find it.
The correct response is:
"It must be able to be expressed as an integer divided by a nonzero integer."
To understand why this condition is necessary for a number to be rational, we need to understand what rational numbers are.
Rational numbers are numbers that can be written as a fraction, where both the numerator and denominator are integers. The condition mentioned means that a rational number can be expressed as a ratio of two integers.
For example, 1/2, 3/4, and -5/2 are all rational numbers because they can be expressed as a fraction with integers as numerator and denominator.
However, numbers like π (pi) and √2 (square root of 2) are not rational numbers because they cannot be expressed as a ratio of two integers. These numbers are called irrational numbers.
So, to determine if a number is rational, you need to check if it can be expressed as an integer divided by a nonzero integer. If it can, then it is rational; otherwise, it is irrational.
Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It does not exist.
It does not exist.
It is equal to 1.
It is equal to 1.
It requires a computer to find it.
It requires a computer to find it.
It involves large numbers.