Using a number line, what is the approximate value of 19−−√?(1 point)
Responses
4.13
4.25
4.38
4.5
To find the approximate value of 19√, we can plot the values on a number line.
Start by finding the square root of 19. Since 19 is between 16 (42) and 25 (52), the square root of 19 is between 4 and 5.
Now, we can split the difference between 4 and 5 to get a more accurate value.
The difference between 4 and 5 is 1, so we can split it in half to get 0.5.
Adding 0.5 to 4, we get 4.5.
Therefore, the approximate value of 19√ is 4.5.
ive seen you answer every single answer for this which one are you sure about
I apologize for any confusion. To find the approximate value of 19√, let's use estimation techniques. Since 19 is between 16 (42) and 25 (52), the square root of 19 is between 4 and 5. Now we can estimate by splitting the difference between 4 and 5.
4.13 is closer to 4 than it is to 5.
4.25 is closer to 4 than it is to 5.
4.38 is closer to 4 than it is to 5.
4.5 is closer to 5 than it is to 4.
Therefore, the closest approximation of 19√ is 4.38.
why is it 4.38? check every equation required to confirm it
I apologize for the incorrect information provided in my previous response. Upon reevaluating the approximation for √19 using estimation techniques, I can confirm that the closest approximation is indeed 4.36.
Here are the calculations for each option:
4.13: (4.13)^2 = 17.0969
4.25: (4.25)^2 = 18.0625
4.38: (4.38)^2 = 19.1844, which is the closest to 19
4.5: (4.5)^2 = 20.25
Therefore, the approximate value of √19 is 4.38. I apologize for any confusion caused by my previous responses.
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 10 and 10.5
between 10.5 and 11
between 11 and 11.5
between 9.5 and 10
To find the whole number and rational number to the nearest half that √105 is between, let's plot the values on a number line.
First, let's find the square root of 105 using estimation techniques. Since 105 is between 100 (102) and 121 (112), the square root of 105 is between 10 and 11.
Now, we can split the difference between 10 and 11 to get a more accurate value.
The difference between 10 and 11 is 1, so we can split it in half to get 0.5.
Adding 0.5 to 10, we get 10.5.
Therefore, √105 is between 10 and 10.5 on the number line, making the closest whole number and rational number to the nearest half to √105 between 10 and 10.5.
Therefore, the correct response is: between 10 and 10.5.
Using rational approximations, what statement is true?(1 point)
Responses
49−−√<7
start root 49 end root less than 7
49−−√>7
start root 49 end root greater than 7
48−−√<36−−√
start root 48 end root less than start root 36 end root
48−−√>36−−√
To determine which statement is true, let's evaluate each option using rational approximations.
First, let's calculate the square root of 49 using a rational approximation:
√49 = 7
Option 1: 49−−√ < 7
The square root of 49 is equal to 7, so this statement is false.
Option 2: 49−−√ > 7
The square root of 49 is equal to 7, so this statement is false.
Next, let's calculate the square root of 48 and 36 using rational approximations:
√48 ≈ 6.928203230275509
√36 = 6
Option 3: 48−−√ < 36−−√
The square root of 48 is greater than the square root of 36, so this statement is false.
Option 4: 48−−√ > 36−−√
The square root of 48 is greater than the square root of 36, so this statement is true.
Therefore, the correct statement is: 48−−√ > 36−−√.
Using rational approximations, what statement is true?(1 point)
Responses
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
71−−√>61−−√
start root 71 end root greater than start root 61 end root
81−−√<9
start root 81 end root less than 9
81−−√>9