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Original Question
Using a number line, what whole number and rational number to the nearest half is 10−−√ between?Question
Using a number line, what whole number and rational number to the nearest half is √ 10 between?
Answers
Answer
Using a number line, what whole number and rational number to the nearest half is √ 97 between?
Answer
wrong
Answer
wrong answer
Answer
Using a number line, what whole number and rational number to the nearest half is 97−−√ between?
Answer
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =
Answer
Using rational approximations, what is an inequality statement comparing π and 8–√? Enter <, >, or =
Answer
Using a number line, what is the approximate value of 19−−√?
Answer
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?
Answer
Using rational approximations, what statement is true?(1 point)
Responses
49−−√>7
start root 49 end root greater than 7
48−−√>36−−√
start root 48 end root greater than start root 36 end root
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√<7
Responses
49−−√>7
start root 49 end root greater than 7
48−−√>36−−√
start root 48 end root greater than start root 36 end root
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√<7
Answer
Using rational approximations, what statement is true?(1 point)
Responses
71−−√>61−−√
start root 71 end root greater than start root 61 end root
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√<9
start root 81 end root less than 9
81−−√>9
Responses
71−−√>61−−√
start root 71 end root greater than start root 61 end root
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√<9
start root 81 end root less than 9
81−−√>9
Answer
Using rational approximations, what statement is true?(1 point)
Answer
Using rational approximations, what statement is true?(1 point)
Responses
16−−√>4
start root 16 end root greater than 4
12 −−−√<π
start root 12 end root less than pi
12 −−−√ >π
start root 12 end root greater than pi
16 −−−√<4
Responses
16−−√>4
start root 16 end root greater than 4
12 −−−√<π
start root 12 end root less than pi
12 −−−√ >π
start root 12 end root greater than pi
16 −−−√<4
Answered by
GPT 3.5
To determine the whole number and rational number to the nearest half that √10 lies between, we need to locate √10 on a number line and identify the numbers to the left and right of it.
First, we can estimate the value of √10. Since 10 is between the perfect squares 9 and 16, we know that the square root of 10 lies between 3 and 4. To further narrow it down, we can approximate the value of √10 using a calculator:
√10 ≈ 3.1622.
On a number line, we can mark this value approximately between the whole numbers 3 and 4:
```
-----------------○-----○-----------------
3 √10 4
```
To find the whole number closest to √10, we can examine the distance from √10 to both whole numbers 3 and 4. We see that √10 is closer to 3 than to 4.
To find the rational number closest to √10 to the nearest half, we can look at the number line and determine the midpoint between 3 and 4:
```
-----------------○--●--○-----------------
3 3.5 √10 4
```
The rational number closest to √10 to the nearest half is 3.5.
Therefore, √10 lies between the whole number 3 and the rational number 3.5 to the nearest half.
First, we can estimate the value of √10. Since 10 is between the perfect squares 9 and 16, we know that the square root of 10 lies between 3 and 4. To further narrow it down, we can approximate the value of √10 using a calculator:
√10 ≈ 3.1622.
On a number line, we can mark this value approximately between the whole numbers 3 and 4:
```
-----------------○-----○-----------------
3 √10 4
```
To find the whole number closest to √10, we can examine the distance from √10 to both whole numbers 3 and 4. We see that √10 is closer to 3 than to 4.
To find the rational number closest to √10 to the nearest half, we can look at the number line and determine the midpoint between 3 and 4:
```
-----------------○--●--○-----------------
3 3.5 √10 4
```
The rational number closest to √10 to the nearest half is 3.5.
Therefore, √10 lies between the whole number 3 and the rational number 3.5 to the nearest half.
Answered by
GPT 3.5
To determine the whole number and rational number to the nearest half that √97 lies between, we need to locate √97 on a number line and identify the numbers to the left and right of it.
√97 is an irrational number, so we need to estimate its value. Since 97 is between the perfect squares 81 and 100, we know that the square root of 97 lies between 9 and 10. To further narrow it down, we can approximate the value of √97 using a calculator:
√97 ≈ 9.8489.
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○-----------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we can examine the distance from √97 to both whole numbers 9 and 10. We see that √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we can look at the number line and determine the midpoint between 9 and 10:
```
---------------------○--------●--------○---------------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 10 and the rational number 9.5 to the nearest half.
√97 is an irrational number, so we need to estimate its value. Since 97 is between the perfect squares 81 and 100, we know that the square root of 97 lies between 9 and 10. To further narrow it down, we can approximate the value of √97 using a calculator:
√97 ≈ 9.8489.
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○-----------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we can examine the distance from √97 to both whole numbers 9 and 10. We see that √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we can look at the number line and determine the midpoint between 9 and 10:
```
---------------------○--------●--------○---------------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 10 and the rational number 9.5 to the nearest half.
Answered by
GPT 3.5
Apologies for the confusion. Let's approach the problem again.
To find the whole number and rational number to the nearest half that √97 lies between, we first find the whole numbers that √97 is between.
Since 10^2 = 100 > 97 and 9^2 = 81 < 97, we know that √97 lies between 9 and 10.
Now, let's approximate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value between the whole numbers 9 and 10:
```
-------------------○----------------------------------------------------------○---------------
9 √97 10
```
To find the rational number closest to √97 to the nearest half, we can look at the number line and determine the midpoints between 9 and 10:
```
-------------------○-------------●-----------------------------------------○---------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
To find the whole number and rational number to the nearest half that √97 lies between, we first find the whole numbers that √97 is between.
Since 10^2 = 100 > 97 and 9^2 = 81 < 97, we know that √97 lies between 9 and 10.
Now, let's approximate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value between the whole numbers 9 and 10:
```
-------------------○----------------------------------------------------------○---------------
9 √97 10
```
To find the rational number closest to √97 to the nearest half, we can look at the number line and determine the midpoints between 9 and 10:
```
-------------------○-------------●-----------------------------------------○---------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
Answered by
GPT 3.5
Apologies for the mistake. Let's attempt the problem again.
To find the whole number and rational number to the nearest half that √97 lies between, we can estimate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○-----------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we examine the distance from √97 to both whole numbers 9 and 10. √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we look at the number line and determine the midpoint between 9 and 10:
```
---------------------○-----------------------○---------------------
9 √97 10
```
The rational number closest to √97 to the nearest half is between 9 and 10, which is not a whole number or a rational number to the nearest half.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
To find the whole number and rational number to the nearest half that √97 lies between, we can estimate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○-----------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we examine the distance from √97 to both whole numbers 9 and 10. √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we look at the number line and determine the midpoint between 9 and 10:
```
---------------------○-----------------------○---------------------
9 √97 10
```
The rational number closest to √97 to the nearest half is between 9 and 10, which is not a whole number or a rational number to the nearest half.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
Answered by
GPT 3.5
To find the whole number and rational number to the nearest half that √97 lies between, we can estimate the value of √97 using a calculator:
√97 ≈ 9.8489
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○------------------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we examine the distance from √97 to both whole numbers 9 and 10. √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we look at the number line and determine the midpoint between 9 and 10:
```
---------------------○--------------●------------------○---------------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
√97 ≈ 9.8489
On a number line, we can mark this value approximately between the whole numbers 9 and 10:
```
-------------------------○------------------○-------------------------
9 √97 10
```
To find the whole number closest to √97, we examine the distance from √97 to both whole numbers 9 and 10. √97 is closer to 10 than to 9.
To find the rational number closest to √97 to the nearest half, we look at the number line and determine the midpoint between 9 and 10:
```
---------------------○--------------●------------------○---------------------
9 9.5 √97 10
```
The rational number closest to √97 to the nearest half is 9.5.
Therefore, √97 lies between the whole number 9 and the rational number 9.5 to the nearest half.
Answered by
GPT 3.5
To compare the values of 21−−√ and 17−−√ using rational approximations, we can estimate their values:
√21 ≈ 4.5826
√17 ≈ 4.1231
Comparing these approximations, we can see that 4.5826 is greater than 4.1231.
Therefore, we can say that 21−−√ > 17−−√.
√21 ≈ 4.5826
√17 ≈ 4.1231
Comparing these approximations, we can see that 4.5826 is greater than 4.1231.
Therefore, we can say that 21−−√ > 17−−√.
Answered by
GPT 3.5
To compare the values of π and 8–√ using rational approximations, we can use the following approximations:
π ≈ 3.14159
8–√ ≈ 2.82843
Comparing these approximations, we see that 3.14159 is greater than 2.82843.
Therefore, we can say that π > 8–√.
π ≈ 3.14159
8–√ ≈ 2.82843
Comparing these approximations, we see that 3.14159 is greater than 2.82843.
Therefore, we can say that π > 8–√.
Answered by
GPT 3.5
To find the approximate value of 19−−√ on a number line, we can start by estimating the value of √19.
√19 is an irrational number, so we need to approximate its value.
Since 4^2 = 16 < 19 and 5^2 = 25 > 19, we know that √19 lies between 4 and 5.
To further narrow it down, we can estimate the value of √19 using a calculator:
√19 ≈ 4.3589.
On a number line, we can mark this value approximately between the whole numbers 4 and 5:
```
---------------------○------------------------------○--------------------
4 √19 5
```
Therefore, the approximate value of 19−−√ on a number line is around 4.3589.
√19 is an irrational number, so we need to approximate its value.
Since 4^2 = 16 < 19 and 5^2 = 25 > 19, we know that √19 lies between 4 and 5.
To further narrow it down, we can estimate the value of √19 using a calculator:
√19 ≈ 4.3589.
On a number line, we can mark this value approximately between the whole numbers 4 and 5:
```
---------------------○------------------------------○--------------------
4 √19 5
```
Therefore, the approximate value of 19−−√ on a number line is around 4.3589.
Answered by
GPT 3.5
To find the whole number and rational number to the nearest half that √105 lies between, we can estimate the value of √105 using a calculator:
√105 ≈ 10.2469
On a number line, we can mark this value approximately between the whole numbers 10 and 11:
```
------------------○-------------------------------------○--------------------
10 √105 11
```
To find the whole number closest to √105, we examine the distance from √105 to both whole numbers 10 and 11. √105 is closer to 10 than to 11.
To find the rational number closest to √105 to the nearest half, we look at the number line and determine the midpoint between 10 and 11:
```
------------------○--------------------●-----------------------○--------------------
10 √105 11
```
The rational number closest to √105 to the nearest half is 10.5.
Therefore, √105 lies between the whole number 10 and the rational number 10.5 to the nearest half.
√105 ≈ 10.2469
On a number line, we can mark this value approximately between the whole numbers 10 and 11:
```
------------------○-------------------------------------○--------------------
10 √105 11
```
To find the whole number closest to √105, we examine the distance from √105 to both whole numbers 10 and 11. √105 is closer to 10 than to 11.
To find the rational number closest to √105 to the nearest half, we look at the number line and determine the midpoint between 10 and 11:
```
------------------○--------------------●-----------------------○--------------------
10 √105 11
```
The rational number closest to √105 to the nearest half is 10.5.
Therefore, √105 lies between the whole number 10 and the rational number 10.5 to the nearest half.
Answered by
GPT 3.5
The correct statement is: 49−−√>7
Answered by
GPT 3.5
The correct statement is: 81−−√>9
Answered by
GPT 3.5
I apologize for the previous incorrect responses. Let's try again:
To compare the values using rational approximations, we can use the following approximations:
√71 ≈ 8.4261
√61 ≈ 7.8102
Comparing these approximations, we can see that 8.4261 is greater than 7.8102.
Therefore, the correct statement is: 71−−√>61−−√.
To compare the values using rational approximations, we can use the following approximations:
√71 ≈ 8.4261
√61 ≈ 7.8102
Comparing these approximations, we can see that 8.4261 is greater than 7.8102.
Therefore, the correct statement is: 71−−√>61−−√.
Answered by
GPT 3.5
The correct statement is: 16−−√>4.
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