Approximate Values of Irrational Numbers Quick Check
1 of 51 of 5 Items
Question
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
4.38
why does nobody but the bot respond now
ikr, but is it right?? (Date, Friday September 1 2023)
Using rational approximations, what statement is true?(1 point)
Responses
48−−√<36−−√
start root 48 end root less than start root 36 end root
48−−√>36−−√
start root 48 end root greater than start root 36 end root
49−−√<7
start root 49 end root less than 7
49−−√>7
it makes no sense
Bot is stupid
The approximate value of √19 is 4.36. Therefore, the closest option is 4.38.
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 11 and 11.5
between 11 and 11.5
between 10 and 10.5
between 10 and 10.5
between 10.5 and 11
between 10.5 and 11
The approximate value of √105 is approximately 10.24. To find the whole number and nearest rational number to the nearest half, we determine that √105 is between 10 and 11. The rational number to the nearest half would be between 10.5 and 11. Therefore, the correct response is "between 10.5 and 11".
To compare and approximate the values of √48 and √36, we can simplify these square roots to their rational approximations.
√48 can be simplified to √(16 * 3), which is equal to 4√3.
√36 is equal to 6.
Therefore, the correct answer is "48−−√>36−−√" since 4√3 is greater than 6.
Using rational approximations, what statement is true?(1 point)
Responses
81−−√>9
start root 81 end root greater than 9
81−−√<9
start root 81 end root less than 9
71−−√>61−−√
start root 71 end root greater than start root 61 end root
71 −−−√<61−−√
To compare and approximate the values of √81 and √9:
√81 simplifies to 9.
√9 is equal to 3.
Therefore, the correct statement is "81−−√>9" since 9 is greater than 3.
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 greater than pi
16−−√>4
start root 16 end root greater than 4
12 −−−√<π
To compare and approximate the values of √16 and √4:
√16 is equal to 4.
√4 is also equal to 4.
Therefore, the correct statement is "16−−√=4" since both values are equal.
Using a number line, what is the approximate number value of 103−−−√? Provide your answer in decimal form, rounded to the nearest hundredth.(1 point)
103−−−√ is approximately
Using a calculator, we can find that the approximate value of √103 is approximately 10.15. Therefore, rounding to the nearest hundredth, 103−−−√ is approximately 10.15.
Using a number line, what whole number and rational number to the nearest half is 10−−√ between?(1 point)
10−−√ is between
and
To find the whole number and rational number to the nearest half that 10−−√ is between, we can approximate the value of √10.
√10 is approximately 3.16.
Since 3 is the largest whole number less than 3.16 and 3.5 is the nearest half greater than 3.16, the whole number and rational number to the nearest half that 10−−√ is between are 3 and 3.5.
Therefore, 10−−√ is between 3 and 3.5.