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Using a number line, what is the approximate value of 19−−√ ?(1 point) Responses 4.25 4.25 4.13 4.13 4.5 4.5 4.38Asked by cripface
Using a number line, what is the approximate value of 19−−√?(1 point)
Responses
4.5
4.5
4.13
4.13
4.25
4.25
4.38
Responses
4.5
4.5
4.13
4.13
4.25
4.25
4.38
Answers
Answered by
cripface
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 9.5 and 10
between 9.5 and 10
between 10 and 10.5
between 10 and 10.5
between 11 and 11.5
between 11 and 11.5
between 10.5 and 11
Responses
between 9.5 and 10
between 9.5 and 10
between 10 and 10.5
between 10 and 10.5
between 11 and 11.5
between 11 and 11.5
between 10.5 and 11
Answered by
cripface
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
Answered by
cripface
Using rational approximations, what statement is true?(1 point)
Responses
71−−√>61−−√
start root 71 end root greater than start root 61 end root
81−−√>9
start root 81 end root greater than 9
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√<9
Responses
71−−√>61−−√
start root 71 end root greater than start root 61 end root
81−−√>9
start root 81 end root greater than 9
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√<9
Answered by
cripface
Using rational approximations, what statement is true?(1 point)
Responses
12 −−−√<π
start root 12 end root less than pi
16 −−−√<4
start root 16 end root less than 4
16−−√>4
start root 16 end root greater than 4
12 −−−√ >π
Responses
12 −−−√<π
start root 12 end root less than pi
16 −−−√<4
start root 16 end root less than 4
16−−√>4
start root 16 end root greater than 4
12 −−−√ >π
Answered by
GPT-4o mini
To approximate the value of \( \sqrt{19} \) on a number line, we note that:
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
Since \( 16 < 19 < 25 \), it follows that \( 4 < \sqrt{19} < 5 \).
To get a closer approximation, we can evaluate \( 4.4 \) and \( 4.5 \):
- \( 4.4^2 = 19.36 \) (which is greater than 19)
- \( 4.3^2 = 18.49 \) (which is less than 19)
This places \( \sqrt{19} \) between \( 4.3 \) and \( 4.4 \).
Next, let's check \( 4.35 \):
- \( 4.35^2 = 18.9225 \) (less than 19)
Then \( 4.38 \):
- \( 4.38^2 = 19.1844 \) (greater than 19)
From this, we can see that:
- \( 4.35^2 < 19 < 4.4^2 \)
Thus, \( \sqrt{19} \) is approximately \( 4.35 < \sqrt{19} < 4.4 \).
Given all the options provided, the closest to \( \sqrt{19} \) is:
**4.38**
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
Since \( 16 < 19 < 25 \), it follows that \( 4 < \sqrt{19} < 5 \).
To get a closer approximation, we can evaluate \( 4.4 \) and \( 4.5 \):
- \( 4.4^2 = 19.36 \) (which is greater than 19)
- \( 4.3^2 = 18.49 \) (which is less than 19)
This places \( \sqrt{19} \) between \( 4.3 \) and \( 4.4 \).
Next, let's check \( 4.35 \):
- \( 4.35^2 = 18.9225 \) (less than 19)
Then \( 4.38 \):
- \( 4.38^2 = 19.1844 \) (greater than 19)
From this, we can see that:
- \( 4.35^2 < 19 < 4.4^2 \)
Thus, \( \sqrt{19} \) is approximately \( 4.35 < \sqrt{19} < 4.4 \).
Given all the options provided, the closest to \( \sqrt{19} \) is:
**4.38**
Answered by
GPT-4o mini
To determine where \( \sqrt{105} \) falls on a number line, we can first find the squares of whole numbers that are close to 105.
We know:
- \( 10^2 = 100 \)
- \( 11^2 = 121 \)
Since \( 100 < 105 < 121 \), it follows that:
\[
10 < \sqrt{105} < 11
\]
Now, we can check the value of \( 10.5 \):
- \( 10.5^2 = 110.25 \) (which is greater than 105)
This means:
- \( \sqrt{105} < 10.5 \)
Next, let's check \( 10.25 \):
- \( 10.25^2 = 105.0625 \) (which is greater than 105)
Now, check \( 10.2 \):
- \( 10.2^2 = 104.04 \) (which is less than 105)
From this, we find that:
\[
10.2 < \sqrt{105} < 10.25
\]
This provides a more precise range for \( \sqrt{105} \).
Given the options provided, \( \sqrt{105} \) is between:
**between 10 and 10.5**.
We know:
- \( 10^2 = 100 \)
- \( 11^2 = 121 \)
Since \( 100 < 105 < 121 \), it follows that:
\[
10 < \sqrt{105} < 11
\]
Now, we can check the value of \( 10.5 \):
- \( 10.5^2 = 110.25 \) (which is greater than 105)
This means:
- \( \sqrt{105} < 10.5 \)
Next, let's check \( 10.25 \):
- \( 10.25^2 = 105.0625 \) (which is greater than 105)
Now, check \( 10.2 \):
- \( 10.2^2 = 104.04 \) (which is less than 105)
From this, we find that:
\[
10.2 < \sqrt{105} < 10.25
\]
This provides a more precise range for \( \sqrt{105} \).
Given the options provided, \( \sqrt{105} \) is between:
**between 10 and 10.5**.
Answered by
GPT-4o mini
To determine which statement is true, let's evaluate each option:
1. **\( \sqrt{49} > 7 \)**
- \( \sqrt{49} = 7 \)
- Therefore, the statement \( \sqrt{49} > 7 \) is **false**.
2. **\( \sqrt{48} > \sqrt{36} \)**
- \( \sqrt{48} \approx 6.93 \)
- \( \sqrt{36} = 6 \)
- Since \( 6.93 > 6 \), the statement \( \sqrt{48} > \sqrt{36} \) is **true**.
3. **\( \sqrt{48} < \sqrt{36} \)**
- As we found above, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \).
- Thus, the statement \( \sqrt{48} < \sqrt{36} \) is **false**.
4. **\( \sqrt{49} < 7 \)**
- Since \( \sqrt{49} = 7 \), this statement \( \sqrt{49} < 7 \) is **false**.
From the above evaluations, the only true statement is:
**\( \sqrt{48} > \sqrt{36} \)**.
1. **\( \sqrt{49} > 7 \)**
- \( \sqrt{49} = 7 \)
- Therefore, the statement \( \sqrt{49} > 7 \) is **false**.
2. **\( \sqrt{48} > \sqrt{36} \)**
- \( \sqrt{48} \approx 6.93 \)
- \( \sqrt{36} = 6 \)
- Since \( 6.93 > 6 \), the statement \( \sqrt{48} > \sqrt{36} \) is **true**.
3. **\( \sqrt{48} < \sqrt{36} \)**
- As we found above, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \).
- Thus, the statement \( \sqrt{48} < \sqrt{36} \) is **false**.
4. **\( \sqrt{49} < 7 \)**
- Since \( \sqrt{49} = 7 \), this statement \( \sqrt{49} < 7 \) is **false**.
From the above evaluations, the only true statement is:
**\( \sqrt{48} > \sqrt{36} \)**.
Answered by
GPT-4o mini
Let's evaluate each statement to determine which is true.
1. **\( \sqrt{71} > \sqrt{61} \)**
- Since \( 71 > 61 \), we can conclude that \( \sqrt{71} > \sqrt{61} \) is **true**.
2. **\( \sqrt{81} > 9 \)**
- \( \sqrt{81} = 9 \)
- Therefore, the statement \( \sqrt{81} > 9 \) is **false**.
3. **\( \sqrt{71} < \sqrt{61} \)**
- This is the opposite of the first statement. Since we have already established that \( \sqrt{71} > \sqrt{61} \), this statement is **false**.
4. **\( \sqrt{81} < 9 \)**
- Again, since \( \sqrt{81} = 9 \), the statement \( \sqrt{81} < 9 \) is **false**.
Based on this evaluation, the true statement is:
**\( \sqrt{71} > \sqrt{61} \)**.
1. **\( \sqrt{71} > \sqrt{61} \)**
- Since \( 71 > 61 \), we can conclude that \( \sqrt{71} > \sqrt{61} \) is **true**.
2. **\( \sqrt{81} > 9 \)**
- \( \sqrt{81} = 9 \)
- Therefore, the statement \( \sqrt{81} > 9 \) is **false**.
3. **\( \sqrt{71} < \sqrt{61} \)**
- This is the opposite of the first statement. Since we have already established that \( \sqrt{71} > \sqrt{61} \), this statement is **false**.
4. **\( \sqrt{81} < 9 \)**
- Again, since \( \sqrt{81} = 9 \), the statement \( \sqrt{81} < 9 \) is **false**.
Based on this evaluation, the true statement is:
**\( \sqrt{71} > \sqrt{61} \)**.
Answered by
GPT-4o mini
To evaluate the statements, let's find the approximate values for \( \sqrt{12} \) and \( \pi \), as well as the exact value for \( \sqrt{16} \):
1. **Calculate \( \sqrt{12} \)**:
- \( \sqrt{12} \approx 3.464 \)
2. **\( \pi \)**:
- \( \pi \approx 3.14159 \)
3. **Calculate \( \sqrt{16} \)**:
- \( \sqrt{16} = 4 \)
Now, let's evaluate the statements:
1. **\( \sqrt{12} < \pi \)**
- \( 3.464 < 3.14159 \) is **false**.
2. **\( \sqrt{16} < 4 \)**
- \( 4 < 4 \) is **false**.
3. **\( \sqrt{16} > 4 \)**
- \( 4 > 4 \) is **false**.
4. **\( \sqrt{12} > \pi \)**
- \( 3.464 > 3.14159 \) is **true**.
Based on the evaluations, the true statement is:
**\( \sqrt{12} > \pi \)**.
1. **Calculate \( \sqrt{12} \)**:
- \( \sqrt{12} \approx 3.464 \)
2. **\( \pi \)**:
- \( \pi \approx 3.14159 \)
3. **Calculate \( \sqrt{16} \)**:
- \( \sqrt{16} = 4 \)
Now, let's evaluate the statements:
1. **\( \sqrt{12} < \pi \)**
- \( 3.464 < 3.14159 \) is **false**.
2. **\( \sqrt{16} < 4 \)**
- \( 4 < 4 \) is **false**.
3. **\( \sqrt{16} > 4 \)**
- \( 4 > 4 \) is **false**.
4. **\( \sqrt{12} > \pi \)**
- \( 3.464 > 3.14159 \) is **true**.
Based on the evaluations, the true statement is:
**\( \sqrt{12} > \pi \)**.