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
4.38
4.38
To find the approximate value of √19, we can look for the number on the number line that is closest to the square root of 19.
Approximately, √19 is between 4.12 and 4.13 on the number line.
Therefore, the approximate value of √19 is 4.13.
So, the correct answer is 4.13.
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 10 and 10.5
between 10 and 10.5
between 9.5 and 10
between 9.5 and 10
between 11 and 11.5
To find the whole number and rational number to the nearest half that is closest to √105, we can use a number line.
√105 is approximately between 10 and 11 on the number line.
To find the number to the nearest half, we look for the number that is halfway between 10 and 11, which is 10.5.
Therefore, the whole number and rational number to the nearest half that is closest to √105 is between 10 and 10.5.
So, the correct answer is between 10 and 10.5.
Using rational approximations, what statement is true?(1 point)
Responses
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√>7
start root 49 end root greater than 7
49−−√<7
start root 49 end root less than 7
48−−√>36−−√
To compare the values of √48 and √36 using rational approximations, we can find the closest whole numbers that are less than or greater than the square roots.
√48 is approximately between 6 and 7 on the number line, while √36 is exactly equal to 6.
Therefore, the statement that is true is:
√48 > √36
So, the correct answer is 48−−√>36−−√.
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
81−−√<9
start root 81 end root less than 9
71 −−−√<61−−√
To compare the values of √71 and √61 using rational approximations, we can find the closest whole numbers that are less than or greater than the square roots.
√71 is approximately between 8 and 9 on the number line, while √61 is approximately between 7 and 8 on the number line.
Therefore, the statement that is true is:
√71 > √61.
So, the correct answer is 71−−√>61−−√.
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
16−−√>4
start root 16 end root greater than 4
12 −−−√ >π
To compare the values of √16 and 4 using rational approximations, we can find the closest whole numbers that are less than or greater than the square roots.
√16 is exactly equal to 4 on the number line.
Therefore, the statement that is true is:
√16 = 4
So, the correct answer is 16−−√=4.
To find the approximate value of 19−−√ using a number line, we need to estimate where the square root value falls between two whole numbers.
Start by identifying two whole numbers on either side of 19, for example, 4 and 5.
Now think about the square roots of these numbers. The square root of 4 is 2, and the square root of 5 is approximately 2.24.
Since we need to find the square root of 19, which is somewhere between 4 and 5, we can estimate a value between 2.24 and 2.5.
Looking at the given options, the closest value to this estimate is 4.38. Therefore, the approximate value of 19−−√ on a number line is 4.38.