Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
what are all of the answers?
To find a whole number and rational number to the nearest half that is between the numbers, we need to determine the numbers that are on either side of √105 on the number line.
To do this, we can find the whole number and the closest whole number to the left and right of √105. Since √105 is between 10 (whose square is 100) and 11 (whose square is 121), we can determine that the closest whole numbers are 10 and 11.
To find the rational number nearest to the half, we can average 10 and 11:
(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5
Therefore, the whole number nearest to √105 is 10, and the rational number to the nearest half is 10.5.
is 12√<π
To determine if √12 is less than π, we can compare the values of each number.
The square root of 12 is approximately 3.464. Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter, and its approximate value is 3.14159.
Comparing the values, we find that √12 is greater than π, since 3.464 > 3.14159.
Therefore, 12√π is not less than π.
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
12 −−−√ >π
start root 12 end root greater than pi
16−−√>4
To compare these expressions, we can evaluate the square roots and compare the values.
The square root of 12 is approximately 3.464. Pi (π) is approximately 3.14159.
Comparing the values, we find that √12 is greater than π, since 3.464 > 3.14159.
Therefore, the statement "√12 > π" is true.
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−−√
To compare these expressions, we can evaluate the square roots and compare the values.
The square root of 81 is 9. The square root of 9 is also 9.
Comparing the values, we find that √81 is equal to 9, and √9 is also equal to 9.
Therefore, the statement "√81 = 9" is true.
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 compare these expressions, we can evaluate the square roots and compare the values.
The square root of 49 is 7. The square root of 7 is approximately 2.646.
Comparing the values, we find that √49 is equal to 7, and √7 is approximately 2.646.
Therefore, the statement "√49 = 7" is true.