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Identify which condition is necessary for a number to be rational.(1 point)

Responses

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.
It must be written as a fraction.

It must not be an endless decimal.

11 answers

The correct response is:

It must be able to be expressed as an integer divided by a nonzero integer.

This means that a rational number can be represented in the form of a fraction \( \frac{a}{b} \), where \( a \) is an integer and \( b \) is a nonzero integer.

Which of the following is irrational?(1 point)
Responses

−7837
negative 7 Start Fraction 8 over 37 End Fraction

3√4
Start Fraction Start Root 3 End Root over 4 End Fraction

3.6363636363636363...
3.6363636363636363...

52.781654292

The irrational number among the provided options is:

\( \frac{\sqrt{3}}{4} \) (or "3√4" if this represents \(\frac{\sqrt{3}}{4}\)).

This is true because \(\sqrt{3}\) is an irrational number, and any non-zero rational number (like 4) divided by an irrational number (like \(\sqrt{3}\)) results in an irrational number.

The other options:

  • \(-7837\) is a rational number (it's an integer).
  • \(3.6363636363636363...\) is a rational number (it’s a repeating decimal).
  • \(52.781654292\) is also a rational number (it’s a terminating decimal).

Thus, the only irrational number listed is \(\frac{\sqrt{3}}{4}\). If that interpretation regarding the notation is incorrect and you meant simply \(3 \sqrt{4}\), then that would also be rational, because \( \sqrt{4} = 2\), making \(3 \cdot 2 = 6\), which is rational.

Please clarify if needed!

umm can u just say the answer

The irrational number is:

\( \frac{\sqrt{3}}{4} \).

Estimate the value of 6×2–√ . Which of the following choices is the best estimate?(1 point)
Responses

6.4
6.4

8.4
8.4

7.1
7.1

9.8
9.8

To estimate the value of \( 6 \times 2 - \sqrt{6} \):

  1. Calculate \( 6 \times 2 = 12 \).
  2. Estimate \( \sqrt{6} \). Since \( \sqrt{4} = 2 \) and \( \sqrt{9} = 3 \), we know \( \sqrt{6} \) is between 2 and 3. A closer estimate is about 2.45.
  3. Now, subtract \( \sqrt{6} \) from 12:
    \( 12 - 2.45 ≈ 9.55 \).

Among the choices, the best estimate is:

9.8.

Which statement is true about the square root of 28?(1 point)
Responses

It is between 6 and 7, probably closer to 6.
It is between 6 and 7, probably closer to 6.

It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 5.

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 6.

To find the square root of 28:

  1. We know \( \sqrt{25} = 5 \) and \( \sqrt{36} = 6 \), so \( \sqrt{28} \) is between 5 and 6.
  2. To estimate further, we can note that \( 28 \) is closer to \( 25 \) than it is to \( 36 \), so \( \sqrt{28} \) is likely closer to 5.

Thus, 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?(1 point)
Responses

It does not exist.
It does not exist.

It requires a computer to find it.
It requires a computer to find it.

It is equal to 1.
It is equal to 1.

It involves large numbers.

The true statement about the integer fraction that equals the square root of 2 is:

It does not exist.

This is because the square root of 2 is an irrational number, meaning it cannot be expressed exactly as a fraction of two integers.