Approximate Values of Irrational Numbers Quick Check
3 of 53 of 5 Items
Question
Using rational approximations, what statement is true?(1 point)
Responses
49−−√>7
start root 49 end root greater than 7
49−−√<7
start root 49 end root less than 7
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
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
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√<9
start root 81 end root less than 9
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 greater than 4
16 −−−√<4
start root 16 end root less than 4
12 −−−√ >π
start root 12 end root greater than pi
start root 48 end root greater than start root 36 end root
To determine the correct statement using rational approximations, we need to simplify each expression and compare them.
1. 49−−√ can be approximated as √49 which equals 7.
2. 48−−√ can be approximated as √48 which is between 6 and 7. Let's approximate it as 6.9.
3. 36−−√ can be approximated as √36 which equals 6.
Therefore, the correct statement is 48−−√<36−−√, since 6.9 is less than 6.