Question
Four people have found the distance in kilometers across a small bridge using different methods.
Their results are given in the table. Order the distances from least to greatest.
(1 point)
Responses
512, 28−−√, 5.5¯¯¯, 234512, 28−−√, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 23428−−√, 512, 5.5¯¯¯, 234
28−−√, 5.5¯¯¯, 234, 51228−−√, 5.5¯¯¯, 234, 512
234 , 5.5¯¯¯, 28−−√, 512
Their results are given in the table. Order the distances from least to greatest.
(1 point)
Responses
512, 28−−√, 5.5¯¯¯, 234512, 28−−√, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 23428−−√, 512, 5.5¯¯¯, 234
28−−√, 5.5¯¯¯, 234, 51228−−√, 5.5¯¯¯, 234, 512
234 , 5.5¯¯¯, 28−−√, 512
Answers
Answer
can you explain what you mean by "sqrt"?
Answer
Also, can you reexplain this?
1. **\( \sqrt{28} \)**
\[
\sqrt{28} \approx 5.29 \quad (\text{since } \sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7} \approx 2 \times 2.64575 \approx 5.29)
\]
2. **5.5¯¯¯ (which we take as 5.5)**
\[
5.5 = 5.5
\]
3. **234**
\[
234 = 234
\]
4. **512**
\[
512 = 512
\]
Now, we will compare the approximated values:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
Now, let's compare:
- \( \sqrt{28} \approx 5.29 < 5.5 \)
- \( 5.5 < 234 \)
- \( 234 < 512 \)
Now, we can order the distances from least to greatest:
1. \( \sqrt{28} \)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the correct order is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
You did the work, but didn't explain.
1. **\( \sqrt{28} \)**
\[
\sqrt{28} \approx 5.29 \quad (\text{since } \sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7} \approx 2 \times 2.64575 \approx 5.29)
\]
2. **5.5¯¯¯ (which we take as 5.5)**
\[
5.5 = 5.5
\]
3. **234**
\[
234 = 234
\]
4. **512**
\[
512 = 512
\]
Now, we will compare the approximated values:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
Now, let's compare:
- \( \sqrt{28} \approx 5.29 < 5.5 \)
- \( 5.5 < 234 \)
- \( 234 < 512 \)
Now, we can order the distances from least to greatest:
1. \( \sqrt{28} \)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the correct order is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
You did the work, but didn't explain.
Answer
you DO know that 512 is actually a fraction, right?
Answer
Can you redo this, but 5/12 is a fraction? Is this too much for you?
### Step 1: Calculate \( \sqrt{28} \)
The expression \( \sqrt{28} \) means "the square root of 28." We can simplify this by breaking down the number:
- **Factoring 28**: We can factor 28 as \( 4 \times 7 \).
- **Applying the Square Root**: The property of square roots states that \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). So:
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7}
\]
- **Calculating the Square Roots**:
- \( \sqrt{4} = 2 \)
- \( \sqrt{7} \) is approximately \( 2.64575 \) (you can find this using a calculator).
Therefore:
\[
\sqrt{28} = 2 \times \sqrt{7} \approx 2 \times 2.64575 \approx 5.29150
\]
For simplicity, we round this to:
\[
\sqrt{28} \approx 5.29
\]
### Step 2: Understanding the Second Value, \( 5.5 \)
The notation \( 5.5¯¯¯ \) means that it is simply \( 5.5 \) (there’s no special operation here). Therefore:
\[
5.5 = 5.5
\]
### Step 3: Identifying the Next Values
For the other values provided:
3. **234**: This value is straightforward:
\[
234 = 234
\]
4. **512**: Similarly, this is:
\[
512 = 512
\]
### Step 4: List the Values for Comparison
Now we have all the values we need, which are approximately:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
### Step 5: Compare the Values
Now let’s compare the calculated approximate values:
- We start with \( \sqrt{28} \approx 5.29 \).
- Next, compare it to \( 5.5 \):
\[
5.29 < 5.5
\]
- Then compare \( 5.5 \) to \( 234 \):
\[
5.5 < 234
\]
- Finally, compare \( 234 \) to \( 512 \):
\[
234 < 512
\]
### Step 6: Order from Least to Greatest
Based on these comparisons, we can now arrange the values from least to greatest:
1. \( \sqrt{28} \) (approximately 5.29)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the final order of the distances from least to greatest is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
If you need further clarification on any specific part, let me know!
### Step 1: Calculate \( \sqrt{28} \)
The expression \( \sqrt{28} \) means "the square root of 28." We can simplify this by breaking down the number:
- **Factoring 28**: We can factor 28 as \( 4 \times 7 \).
- **Applying the Square Root**: The property of square roots states that \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). So:
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7}
\]
- **Calculating the Square Roots**:
- \( \sqrt{4} = 2 \)
- \( \sqrt{7} \) is approximately \( 2.64575 \) (you can find this using a calculator).
Therefore:
\[
\sqrt{28} = 2 \times \sqrt{7} \approx 2 \times 2.64575 \approx 5.29150
\]
For simplicity, we round this to:
\[
\sqrt{28} \approx 5.29
\]
### Step 2: Understanding the Second Value, \( 5.5 \)
The notation \( 5.5¯¯¯ \) means that it is simply \( 5.5 \) (there’s no special operation here). Therefore:
\[
5.5 = 5.5
\]
### Step 3: Identifying the Next Values
For the other values provided:
3. **234**: This value is straightforward:
\[
234 = 234
\]
4. **512**: Similarly, this is:
\[
512 = 512
\]
### Step 4: List the Values for Comparison
Now we have all the values we need, which are approximately:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
### Step 5: Compare the Values
Now let’s compare the calculated approximate values:
- We start with \( \sqrt{28} \approx 5.29 \).
- Next, compare it to \( 5.5 \):
\[
5.29 < 5.5
\]
- Then compare \( 5.5 \) to \( 234 \):
\[
5.5 < 234
\]
- Finally, compare \( 234 \) to \( 512 \):
\[
234 < 512
\]
### Step 6: Order from Least to Greatest
Based on these comparisons, we can now arrange the values from least to greatest:
1. \( \sqrt{28} \) (approximately 5.29)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the final order of the distances from least to greatest is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
If you need further clarification on any specific part, let me know!
Answered by
GPT-4o mini
To order the distances from least to greatest, we first need to evaluate the given values:
1. **\( \sqrt{28} \)**
\[
\sqrt{28} \approx 5.29 \quad (\text{since } \sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7} \approx 2 \times 2.64575 \approx 5.29)
\]
2. **5.5¯¯¯ (which we take as 5.5)**
\[
5.5 = 5.5
\]
3. **234**
\[
234 = 234
\]
4. **512**
\[
512 = 512
\]
Now, we will compare the approximated values:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
Now, let's compare:
- \( \sqrt{28} \approx 5.29 < 5.5 \)
- \( 5.5 < 234 \)
- \( 234 < 512 \)
Now, we can order the distances from least to greatest:
1. \( \sqrt{28} \)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the correct order is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
1. **\( \sqrt{28} \)**
\[
\sqrt{28} \approx 5.29 \quad (\text{since } \sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7} \approx 2 \times 2.64575 \approx 5.29)
\]
2. **5.5¯¯¯ (which we take as 5.5)**
\[
5.5 = 5.5
\]
3. **234**
\[
234 = 234
\]
4. **512**
\[
512 = 512
\]
Now, we will compare the approximated values:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
Now, let's compare:
- \( \sqrt{28} \approx 5.29 < 5.5 \)
- \( 5.5 < 234 \)
- \( 234 < 512 \)
Now, we can order the distances from least to greatest:
1. \( \sqrt{28} \)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the correct order is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
Answered by
GPT-4o mini
Certainly! The term "sqrt" is an abbreviation for "square root."
The square root of a number \( x \) is another number \( y \) such that when \( y \) is multiplied by itself (i.e., \( y \times y \)), the result is \( x \).
For example:
- The square root of 9 is 3 because \( 3 \times 3 = 9 \).
- The square root of 16 is 4 because \( 4 \times 4 = 16 \).
- The square root of 28 is written as \( \sqrt{28} \).
In the earlier example, when I referred to \( \sqrt{28} \), I was calculating the square root of 28, which is approximately 5.29. This value is important when comparing distances in your original question.
If you need any more clarification or have further questions, feel free to ask!
The square root of a number \( x \) is another number \( y \) such that when \( y \) is multiplied by itself (i.e., \( y \times y \)), the result is \( x \).
For example:
- The square root of 9 is 3 because \( 3 \times 3 = 9 \).
- The square root of 16 is 4 because \( 4 \times 4 = 16 \).
- The square root of 28 is written as \( \sqrt{28} \).
In the earlier example, when I referred to \( \sqrt{28} \), I was calculating the square root of 28, which is approximately 5.29. This value is important when comparing distances in your original question.
If you need any more clarification or have further questions, feel free to ask!
Answered by
GPT-4o mini
Certainly! Let’s break down each step in more detail and explain the reasoning behind the calculations and comparisons.
### Step 1: Calculate \( \sqrt{28} \)
The expression \( \sqrt{28} \) means "the square root of 28." We can simplify this by breaking down the number:
- **Factoring 28**: We can factor 28 as \( 4 \times 7 \).
- **Applying the Square Root**: The property of square roots states that \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). So:
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7}
\]
- **Calculating the Square Roots**:
- \( \sqrt{4} = 2 \)
- \( \sqrt{7} \) is approximately \( 2.64575 \) (you can find this using a calculator).
Therefore:
\[
\sqrt{28} = 2 \times \sqrt{7} \approx 2 \times 2.64575 \approx 5.29150
\]
For simplicity, we round this to:
\[
\sqrt{28} \approx 5.29
\]
### Step 2: Understanding the Second Value, \( 5.5 \)
The notation \( 5.5¯¯¯ \) means that it is simply \( 5.5 \) (there’s no special operation here). Therefore:
\[
5.5 = 5.5
\]
### Step 3: Identifying the Next Values
For the other values provided:
3. **234**: This value is straightforward:
\[
234 = 234
\]
4. **512**: Similarly, this is:
\[
512 = 512
\]
### Step 4: List the Values for Comparison
Now we have all the values we need, which are approximately:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
### Step 5: Compare the Values
Now let’s compare the calculated approximate values:
- We start with \( \sqrt{28} \approx 5.29 \).
- Next, compare it to \( 5.5 \):
\[
5.29 < 5.5
\]
- Then compare \( 5.5 \) to \( 234 \):
\[
5.5 < 234
\]
- Finally, compare \( 234 \) to \( 512 \):
\[
234 < 512
\]
### Step 6: Order from Least to Greatest
Based on these comparisons, we can now arrange the values from least to greatest:
1. \( \sqrt{28} \) (approximately 5.29)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the final order of the distances from least to greatest is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
If you need further clarification on any specific part, let me know!
### Step 1: Calculate \( \sqrt{28} \)
The expression \( \sqrt{28} \) means "the square root of 28." We can simplify this by breaking down the number:
- **Factoring 28**: We can factor 28 as \( 4 \times 7 \).
- **Applying the Square Root**: The property of square roots states that \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). So:
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7}
\]
- **Calculating the Square Roots**:
- \( \sqrt{4} = 2 \)
- \( \sqrt{7} \) is approximately \( 2.64575 \) (you can find this using a calculator).
Therefore:
\[
\sqrt{28} = 2 \times \sqrt{7} \approx 2 \times 2.64575 \approx 5.29150
\]
For simplicity, we round this to:
\[
\sqrt{28} \approx 5.29
\]
### Step 2: Understanding the Second Value, \( 5.5 \)
The notation \( 5.5¯¯¯ \) means that it is simply \( 5.5 \) (there’s no special operation here). Therefore:
\[
5.5 = 5.5
\]
### Step 3: Identifying the Next Values
For the other values provided:
3. **234**: This value is straightforward:
\[
234 = 234
\]
4. **512**: Similarly, this is:
\[
512 = 512
\]
### Step 4: List the Values for Comparison
Now we have all the values we need, which are approximately:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
### Step 5: Compare the Values
Now let’s compare the calculated approximate values:
- We start with \( \sqrt{28} \approx 5.29 \).
- Next, compare it to \( 5.5 \):
\[
5.29 < 5.5
\]
- Then compare \( 5.5 \) to \( 234 \):
\[
5.5 < 234
\]
- Finally, compare \( 234 \) to \( 512 \):
\[
234 < 512
\]
### Step 6: Order from Least to Greatest
Based on these comparisons, we can now arrange the values from least to greatest:
1. \( \sqrt{28} \) (approximately 5.29)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \)
Thus, the final order of the distances from least to greatest is:
**\( \sqrt{28}, 5.5, 234, 512 \)**.
If you need further clarification on any specific part, let me know!
Answered by
GPT-4o mini
Thank you for that clarification! If \( 512 \) is intended to be a fraction, then I can better assist you by using that context.
Let's assume the scenario that \( 512 \) represents a fraction and may need to be expressed in some form relative to the other numbers provided.
If \( 512 \) is meant to be represented as a fraction (for example, as \( \frac{512}{1} \)), we still need to compare it with the decimal equivalents of the other expression.
Given the previous values:
1. **\( \sqrt{28} \approx 5.29 \)**
2. **5.5 = 5.5**
3. **234** (which remains as a whole number)
4. **512** (interpreted as a fraction, but still \( 512 \) or \( 512/1 \))
To clarify, \( 512 \) is quite large compared to the others:
### Quick Comparison of Values:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 \) (or \( \frac{512}{1} = 512 \))
### Order from Least to Greatest:
Given these values, the order remains the same:
1. \( \sqrt{28} \) (approximately 5.29)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \) (as \( \frac{512}{1} \))
If \( 512 \) represents a specific fraction (not \( \frac{512}{1} \)), please specify the actual fraction so I can make any necessary adjustments in comparisons or calculations. Thank you for your patience!
Let's assume the scenario that \( 512 \) represents a fraction and may need to be expressed in some form relative to the other numbers provided.
If \( 512 \) is meant to be represented as a fraction (for example, as \( \frac{512}{1} \)), we still need to compare it with the decimal equivalents of the other expression.
Given the previous values:
1. **\( \sqrt{28} \approx 5.29 \)**
2. **5.5 = 5.5**
3. **234** (which remains as a whole number)
4. **512** (interpreted as a fraction, but still \( 512 \) or \( 512/1 \))
To clarify, \( 512 \) is quite large compared to the others:
### Quick Comparison of Values:
- \( \sqrt{28} \approx 5.29 \)
- \( 5.5 = 5.5 \)
- \( 234 = 234 \)
- \( 512 \) (or \( \frac{512}{1} = 512 \))
### Order from Least to Greatest:
Given these values, the order remains the same:
1. \( \sqrt{28} \) (approximately 5.29)
2. \( 5.5 \)
3. \( 234 \)
4. \( 512 \) (as \( \frac{512}{1} \))
If \( 512 \) represents a specific fraction (not \( \frac{512}{1} \)), please specify the actual fraction so I can make any necessary adjustments in comparisons or calculations. Thank you for your patience!
Answered by
GPT-4o mini
Absolutely, let's redo the steps you provided, ensuring that we include \( \frac{5}{12} \) as a fraction if that's one of the values you meant to include alongside the others. However, your original mention of "5.5" could be an interpretation of something else. Let's assume that we are comparing four values:
1. \( \sqrt{28} \)
2. \( \frac{5}{12} \)
3. \( 234 \)
4. \( 512 \)
### Step 1: Calculate \( \sqrt{28} \)
The square root of 28 is calculated as follows:
- **Factoring 28**:
\[
28 = 4 \times 7
\]
- **Applying the Square Root Property**:
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7}
\]
- **Calculating**:
- \( \sqrt{4} = 2 \)
- \( \sqrt{7} \) is approximately \( 2.64575 \).
Thus:
\[
\sqrt{28} = 2 \times \sqrt{7} \approx 2 \times 2.64575 \approx 5.29150
\]
Rounding it:
\[
\sqrt{28} \approx 5.29
\]
### Step 2: Convert \( \frac{5}{12} \) to a Decimal
To compare \( \frac{5}{12} \) to other values, we can convert it to a decimal:
\[
\frac{5}{12} \approx 0.41667 \quad (\text{by performing the division } 5 \div 12)
\]
### Step 3: Identify the Other Values
- **234**: This value remains the same.
\[
234 = 234
\]
- **512**: This value is straightforward as well.
\[
512 = 512
\]
### Step 4: List the Values for Comparison
Now, we can list all the values:
- \( \sqrt{28} \approx 5.29 \)
- \( \frac{5}{12} \approx 0.41667 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
### Step 5: Compare the Values
Now let’s compare these values from least to greatest:
1. \( \frac{5}{12} \approx 0.41667 \) (smallest)
2. \( \sqrt{28} \approx 5.29 \)
3. \( 234 \)
4. \( 512 \) (largest)
### Step 6: Final Order from Least to Greatest
Based on the comparisons, the order from least to greatest is:
1. \( \frac{5}{12} \) (approximately 0.41667)
2. \( \sqrt{28} \) (approximately 5.29)
3. \( 234 \)
4. \( 512 \)
Thus, the final order is:
**\( \frac{5}{12}, \sqrt{28}, 234, 512 \)**.
Thank you for your patience! If I misunderstood any of the values or you have additional parameters to include, please let me know!
1. \( \sqrt{28} \)
2. \( \frac{5}{12} \)
3. \( 234 \)
4. \( 512 \)
### Step 1: Calculate \( \sqrt{28} \)
The square root of 28 is calculated as follows:
- **Factoring 28**:
\[
28 = 4 \times 7
\]
- **Applying the Square Root Property**:
\[
\sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7}
\]
- **Calculating**:
- \( \sqrt{4} = 2 \)
- \( \sqrt{7} \) is approximately \( 2.64575 \).
Thus:
\[
\sqrt{28} = 2 \times \sqrt{7} \approx 2 \times 2.64575 \approx 5.29150
\]
Rounding it:
\[
\sqrt{28} \approx 5.29
\]
### Step 2: Convert \( \frac{5}{12} \) to a Decimal
To compare \( \frac{5}{12} \) to other values, we can convert it to a decimal:
\[
\frac{5}{12} \approx 0.41667 \quad (\text{by performing the division } 5 \div 12)
\]
### Step 3: Identify the Other Values
- **234**: This value remains the same.
\[
234 = 234
\]
- **512**: This value is straightforward as well.
\[
512 = 512
\]
### Step 4: List the Values for Comparison
Now, we can list all the values:
- \( \sqrt{28} \approx 5.29 \)
- \( \frac{5}{12} \approx 0.41667 \)
- \( 234 = 234 \)
- \( 512 = 512 \)
### Step 5: Compare the Values
Now let’s compare these values from least to greatest:
1. \( \frac{5}{12} \approx 0.41667 \) (smallest)
2. \( \sqrt{28} \approx 5.29 \)
3. \( 234 \)
4. \( 512 \) (largest)
### Step 6: Final Order from Least to Greatest
Based on the comparisons, the order from least to greatest is:
1. \( \frac{5}{12} \) (approximately 0.41667)
2. \( \sqrt{28} \) (approximately 5.29)
3. \( 234 \)
4. \( 512 \)
Thus, the final order is:
**\( \frac{5}{12}, \sqrt{28}, 234, 512 \)**.
Thank you for your patience! If I misunderstood any of the values or you have additional parameters to include, please let me know!