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

9 answers

The correct answer is: It must be able to be expressed as an integer divided by a nonzero integer.
Which of the following is irrational?(1 point)

a. 3.6363636363636363...

b. 3√4

c. −7837

d. 52.781654292
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.
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
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
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.
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.
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.
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.