Identify which condition is necessary for a number to be rational.(1 point)
It must not be negative.
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 written as a fraction
The correct answer is: It must be able to be expressed as an integer divided by a nonzero integer.
The correct answer is: b. 3√4. This is because the square root of 4 is not a perfect square, therefore it cannot be expressed as a fraction or a terminating or repeating decimal.
To estimate the value of 6×2–√, we can substitute an estimated value for √2, which is approximately 1.4.
So, 6×2–√ ≈ 6×2–1.4 ≈ 6×0.6 ≈ 3.6.
The best estimate from the given choices is: c. 6.4
To determine which statement is true about the square root of 28, we can estimate its value.
By observing that 5^2 = 25 and 6^2 = 36, we can conclude that the square root of 28 falls between 5 and 6.
Since 28 is closer to 25 than 36, we can infer that the square root of 28 is closer to 5 than 6.
Therefore, the correct statement is: c. It is between 5 and 6, probably closer to 5.
The correct statement 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. It is a non-repeating and non-terminating decimal. Therefore, there is no exact fraction that equals the square root of 2.
Which of the following is irrational?(1 point)
a. 3.6363636363636363...
b. 3√4
c. −7837
d. 52.781654292
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
a. 8.4
b. 7.1
c. 6.4
d. 9.8
Which statement is true about the square root of 28?
a. It is between 5 and 6, probably closer to 6.
b. It is between 6 and 7, 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)
It does not exist.
It requires a computer to find it.
It is equal to 1.
It involves large numbers.
To identify which condition is necessary for a number to be rational, we need to understand what a rational number is. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers and the denominator is not zero.
Now, let's examine each option:
1. "It must not be negative." This condition is not necessary for a number to be rational. Rational numbers can be positive or negative, depending on the value of the numerator and denominator in the fraction representation.
2. "It must be able to be expressed as an integer divided by a nonzero integer." This condition is necessary for a number to be rational. All rational numbers can be represented as a fraction, where the numerator and denominator are integers and the denominator is not zero.
3. "It must not be an endless decimal." This condition is not necessary for a number to be rational. While all rational numbers can be expressed as a finite decimal or a repeating decimal, they can also be expressed as a fraction. Endless decimals, such as irrational numbers like pi or square roots, are not rational.
4. "It must be written as a fraction." This condition is necessary for a number to be rational. All rational numbers can be represented as a fraction, where the numerator and denominator are integers and the denominator is not zero.
Therefore, the correct condition necessary for a number to be rational is "It must be able to be expressed as an integer divided by a nonzero integer."