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 less than 9
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√>9
start root 81 end root greater than 9
Using rational approximations, what statement is true?(1 point)
Responses
12 −−−√<π
start root 12 end root less than pi
12 −−−√ >π
start root 12 end root greater than pi
16−−√>4
start root 16 end root greater than 4
16 −−−√<4
start root 16 end root less than 4
please give the corrct answer
The correct statement is:
start root 16 end root greater than 4
The correct statement is 81−−√>9.
To compare the statements using rational approximations, we need to convert the square roots to decimal approximations.
1. sqrt(71) ≈ 8.43
sqrt(61) ≈ 7.81
Comparing the decimal approximations, we have: 8.43 > 7.81
So, the statement "sqrt(71) > sqrt(61)" is true.
2. sqrt(81) = 9
Comparing with 9, we have: 9 < 9
So, the statement "sqrt(81) < 9" is false.
3. sqrt(71) ≈ 8.43
sqrt(61) ≈ 7.81
Comparing the decimal approximations, we have: 8.43 < 7.81
So, the statement "sqrt(71) < sqrt(61)" is false.
4. sqrt(81) = 9
Comparing with 9, we have: 9 > 9
So, the statement "sqrt(81) > 9" is false.
Based on the comparisons, the true statement is: sqrt(71) > sqrt(61).