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Show an example of an irrational number between 9 and 11. (1 point)

O V10
O v20
O V100
0 199

11 answers

An example of an irrational number between 9 and 11 is \( \sqrt{100} \).

To elaborate:

  • The square root of 100 is 10, which is a rational number, so let’s find another.
  • A true irrational number between 9 and 11 is \( \sqrt{98} \) because \( \sqrt{98} \approx 9.899\), which lies between 9 and 11.

In the context of your provided options, given they are symbolic representations (likely for square roots), \( \sqrt{100} \) (which equals 10) does not satisfy the requirement, but if we were to consider approximate values, \( \sqrt{98} \) is irrational and valid.

Another simple example of an irrational number between 9 and 11 is \( \pi + 6 \) (approximately 9.14) or \( e + 8 \) (approximately 10.72).

What’s the answer b

Based on the options you provided (O V10, O v20, O V100, 0 199), it seems like they may represent square roots or symbolic representations.

If we interpret them as follows:

  • O V10 could represent √10
  • O V20 could represent √20
  • O V100 could represent √100
  • 0 199 may not represent a square root and could be a typographical error.

Here’s the evaluation:

  1. √10 is approximately 3.162, which is not between 9 and 11.
  2. √20 is approximately 4.472, which is also not between 9 and 11.
  3. √100 equals 10, which is a whole number between 9 and 11.
  4. 0 199 is unclear.

Therefore, O V100 (√100) is the only option that corresponds directly to a value between 9 and 11.

If the question is asking for an irrational number specifically, you might consider something like \( \sqrt{98} \) instead, but from the options given, O V100 (10) is the appropriate choice.

What is the least integer whose sc root is an irrational number betwe and 7? (1 point)
• 25
• 13
• 26
6

To find the least integer whose square root is an irrational number between 7 and 8, we need to look for integers between \(7^2\) (which is 49) and \(8^2\) (which is 64). The numbers should be non-perfect squares to ensure their square roots are irrational.

Let's evaluate the given options:

  1. 25: \( \sqrt{25} = 5\) (not between 7 and 8)
  2. 13: \( \sqrt{13} \approx 3.605\) (not between 7 and 8)
  3. 26: \( \sqrt{26} \approx 5.099\) (not between 7 and 8)
  4. 6: \( \sqrt{6} \approx 2.449\) (not between 7 and 8)

All of these options yield square roots that are not between 7 and 8.

To find the least integer with an irrational square root between 7 and 8, we need a perfect square just greater than 49 but less than 64. That would be integers like 50, 51, 52, ..., and 63.

Among these, the smallest integer is:

  • 50: \( \sqrt{50} \approx 7.071\) (this is irrational and lies between 7 and 8).

But since 50 is not one of the options listed, none of the four options given (25, 13, 26, 6) are the answer.

If you need to choose from these specific options, the correct answer based on your available number choices is None; however, the least integer providing an irrational square root between 7 and 8, which is not among your options listed, would actually be 50.

50 is not on the menu blud

I apologize for the misunderstanding. Let's re-evaluate the options you provided:

  • 25
  • 13
  • 26
  • 6

We want to find the least integer whose square root is an irrational number between 7 and 8.

Considering the possible values:

  1. For 25:

    • \( \sqrt{25} = 5\) (which is not between 7 and 8).

  2. For 13:

    • \( \sqrt{13} \approx 3.605\) (which is not between 7 and 8).

  3. For 26:

    • \( \sqrt{26} \approx 5.099\) (which is not between 7 and 8).

  4. For 6:

    • \( \sqrt{6} \approx 2.449\) (which is not between 7 and 8).

Since none of the provided options yield a square root between 7 and 8, let's clarify.

To summarize:

  • The integer needs to be between \(49\) (which is \(7^2\)) and \(64\) (which is \(8^2\)).
  • However, looking only at provided integers, none of them (25, 13, 26, 6) meet the criteria for an irrational square root within that range.

The correct point to highlight is that none of the options meet the criteria for having an irrational square root between 7 and 8.

But if I had to derive an answer from the available choices under the original question constraints, I would point out that none fit correctly—thanks for your patience! If you meant for the least integer greater than \(49\) that was also irrational, it would need to be considered \(50\), but since that wasn't provided, your question does not align well with any of the provided choices.

(1 point)
• 25
• 13
• 26
6

I apologize for any confusion earlier. Let's re-evaluate your question to find the least integer among the options given whose square root is an irrational number between 7 and 8.

The relevant information is:

  • The square root must be greater than 7 and less than 8.
  • This translates to the square of the numbers we are considering, meaning we are looking for numbers that are greater than \(7^2 = 49\) and less than \(8^2 = 64\).

Now, let's consider your options again:

  1. 25: \( \sqrt{25} = 5\) (not between 7 and 8).
  2. 13: \( \sqrt{13} \approx 3.605\) (not between 7 and 8).
  3. 26: \( \sqrt{26} \approx 5.099\) (not between 7 and 8).
  4. 6: \( \sqrt{6} \approx 2.449\) (not between 7 and 8).

None of the given options (25, 13, 26, or 6) yield a square root that lies between 7 and 8.

To summarize, if we are looking strictly for the least integer whose square root is irrational and lies between 7 and 8, this integer is \(50\). However, that option is not present in your list.

Since none of your options work for the criteria set, the correct conclusion is that none of these integers meet the requirement.

If there is a specific approach or further instructions you have in mind, please let me know!

Which irrational number is between
V14 and V18? (1 point)
O V15
• /10
O V19
O V13

To find which irrational number is between \( \sqrt{14} \) and \( \sqrt{18} \), we first calculate these square roots approximately:

  1. Calculating \( \sqrt{14} \):

    • \( \sqrt{14} \approx 3.742 \)

  2. Calculating \( \sqrt{18} \):

    • \( \sqrt{18} = \sqrt{9 \times 2} = 3 \sqrt{2} \approx 4.243 \)

Now, we want to find an option that lies between approximately \( 3.742 \) and \( 4.243 \).

Evaluating the Options:

  1. \( \sqrt{15} \):

    • \( \sqrt{15} \approx 3.873 \) (which is between \( \sqrt{14} \) and \( \sqrt{18} \))

  2. \( \sqrt{10} \):

    • \( \sqrt{10} \approx 3.162 \) (which is not between \( \sqrt{14} \) and \( \sqrt{18} \))

  3. \( \sqrt{19} \):

    • \( \sqrt{19} \approx 4.358 \) (which is not between \( \sqrt{14} \) and \( \sqrt{18} \))

  4. \( \sqrt{13} \):

    • \( \sqrt{13} \approx 3.606 \) (which is not between \( \sqrt{14} \) and \( \sqrt{18} \))

Conclusion:

The only option that lies between \( \sqrt{14} \) and \( \sqrt{18} \) is \( \sqrt{15} \).

So, the answer is:

\( \sqrt{15} \).