To find the approximate value of the square root of 19, we can estimate its value on a number line. In this case, we can find the whole number closest to the square root of 19, which is 4. Then, we can estimate the decimal part.
First, we know that the square root of 16 is 4, and the square root of 25 is 5. Since 19 is closer to 16 than 25, we know that the square root of 19 will be slightly larger than 4 but less than 5.
To estimate the decimal part, we can divide the distance between 16 and 19 into 10 equal parts. Each part will be approximately 0.3. Looking at the number line, we can estimate that the square root of 19 is approximately 4.3.
However, none of the answer choices provided match this estimate. The closest option is 4.13, which is also reasonable for the approximation of the square root of 19 on a number line. Therefore, the approximate value of 19−−√ is 4.13.
Using a number line, what is the approximate value of 19−−√?(1 point)
4.13
4.5
4.38
4.25
11 answers
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 10.5 and 11
between 10.5 and 11
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
Responses
between 10.5 and 11
between 10.5 and 11
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
To find the whole number and rational number to the nearest half that 105−−−√ is between, we can use estimation on a number line.
First, we know that the square root of 100 is 10, and the square root of 121 is 11. Since 105 is closer to 121 than 100, we know that the square root of 105 will be slightly larger than 10 but less than 11.
To estimate the decimal part, we can divide the distance between 100 and 105 into 10 equal parts. Each part will be approximately 0.5. Looking at the number line, we can estimate that the square root of 105 is approximately 10.5.
Now, we need to find the whole number and rational number to the nearest half that 105−−−√ is between. Since the square root of 105 is approximately 10.5, the whole number to the nearest half that it is between is 10.
Therefore, the whole number and rational number to the nearest half that 105−−−√ is between is between 10 and 10.5, which is answer choice "between 10 and 10.5".
First, we know that the square root of 100 is 10, and the square root of 121 is 11. Since 105 is closer to 121 than 100, we know that the square root of 105 will be slightly larger than 10 but less than 11.
To estimate the decimal part, we can divide the distance between 100 and 105 into 10 equal parts. Each part will be approximately 0.5. Looking at the number line, we can estimate that the square root of 105 is approximately 10.5.
Now, we need to find the whole number and rational number to the nearest half that 105−−−√ is between. Since the square root of 105 is approximately 10.5, the whole number to the nearest half that it is between is 10.
Therefore, the whole number and rational number to the nearest half that 105−−−√ is between is between 10 and 10.5, which is answer choice "between 10 and 10.5".
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
To compare the rational approximations, we can find the square roots of 49 and 36 using calculator or long division method.
The square root of 49 is 7.
The square root of 36 is 6.
Therefore, we can conclude that 49−−√ is greater than 7, so the statement "49−−√>7" is true.
None of the other statements are true based on the rational approximations.
The square root of 49 is 7.
The square root of 36 is 6.
Therefore, we can conclude that 49−−√ is greater than 7, so the statement "49−−√>7" is true.
None of the other statements are true based on the rational approximations.
Using rational approximations, what statement is true?(1 point)
Responses
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
start root 81 end root less than 9
71−−√>61−−√
start root 71 end root greater than start root 61 end root
Responses
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
start root 81 end root less than 9
71−−√>61−−√
start root 71 end root greater than start root 61 end root
To compare the rational approximations, we can find the square roots of 81 and 9 using calculator or long division method.
The square root of 81 is 9.
The square root of 9 is 3.
Therefore, we can conclude that 81−−√ is greater than 9, so the statement "81−−√>9" is true.
None of the other statements are true based on the rational approximations.
The square root of 81 is 9.
The square root of 9 is 3.
Therefore, we can conclude that 81−−√ is greater than 9, so the statement "81−−√>9" is true.
None of the other statements are true based on the rational approximations.
Question
Using rational approximations, what statement is true?(1 point)
Responses
16 −−−√<4
start root 16 end root less than 4
12 −−−√<π
start root 12 end root less than pi
12 −−−√ >π
start root 12 end root greater than pi
16−−√>41 point)
Using rational approximations, what statement is true?(1 point)
Responses
16 −−−√<4
start root 16 end root less than 4
12 −−−√<π
start root 12 end root less than pi
12 −−−√ >π
start root 12 end root greater than pi
16−−√>41 point)
To compare the rational approximations, we can find the square root of 16 using a calculator or long division method.
The square root of 16 is 4.
Therefore, we can conclude that 16−−−√ is equal to 4.
Based on this information, we can determine that the statement "16−−−√<4" is false.
None of the other statements are true based on the rational approximations.
The square root of 16 is 4.
Therefore, we can conclude that 16−−−√ is equal to 4.
Based on this information, we can determine that the statement "16−−−√<4" is false.
None of the other statements are true based on the rational approximations.
Question
Using rational approximations, what statement is true?(1 point)
Responses
16 −−−√<4
start root 16 end root less than 4
12 −−−√<π
start root 12 end root less than pi
12 −−−√ >π
start root 12 end root greater than pi
16−−√>4
Using rational approximations, what statement is true?(1 point)
Responses
16 −−−√<4
start root 16 end root less than 4
12 −−−√<π
start root 12 end root less than pi
12 −−−√ >π
start root 12 end root greater than pi
16−−√>4
To compare the rational approximations, we can find the square root of 16 using a calculator or long division method.
The square root of 16 is 4.
Therefore, we can conclude that 16−−−√ is equal to 4.
Based on this information, we can determine that the statement "16−−−√>4" is true.
None of the other statements are true based on the rational approximations.
The square root of 16 is 4.
Therefore, we can conclude that 16−−−√ is equal to 4.
Based on this information, we can determine that the statement "16−−−√>4" is true.
None of the other statements are true based on the rational approximations.
6 answers