Using rational approximations, what statement is true?(1 point)
Responses
81−−√<9
start root 81 end root less than 9
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
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
12 −−−√<π
start root 12 end root less than pi
16−−√>4
start root 16 end root greater than 4
start root 71 end root less than start root 61 end root
To determine which statement is true using rational approximations, we can approximate the given square roots and compare them:
1. 81−−√ < 9: To approximate √81, we can use the fact that 9^2 = 81. Therefore, √81 is approximately equal to 9. This statement is false because 9 is not less than 9.
2. 71−−√ > 61−−√: To approximate √71 and √61, we can use the fact that 8^2 = 64 and 7^2 = 49. Therefore, √71 is slightly greater than 8 and √61 is slightly greater than 7. This statement is true because a slightly greater number (√71) is indeed greater than a slightly smaller number (√61).
3. 81−−√ > 9: As mentioned before, √81 is equal to 9. This statement is true because 9 is greater than 9.
4. 71−−√ < 61−−√: Using the same approximations as before, we have √71 > √61. Thus, this statement is false.
Therefore, the true statement using rational approximations is 71−−√ > 61−−√.