Using rational approximations, what statement is true?(1 point)
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√>9
start root 81 end root greater than 9
71−−√>61−−√
start root 71 end root greater than start root 61 end root
81−−√<9
start root 81 end root less than 9
The statement that is true using rational approximations is:
71 −−−√ < 61−−√ (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 values under the square roots.
Let's calculate the rational approximations for each expression:
1) √71 ≈ 8.44
√61 ≈ 7.81
Giving us the expression: 8.44 < 7.81
2) √81 ≈ 9
Giving us the expression: 9 > 9
3) √71 ≈ 8.44
√61 ≈ 7.81
Giving us the expression: 8.44 > 7.81
4) √81 ≈ 9
Giving us the expression: 9 < 9
Now let's evaluate each statement:
1) 8.44 < 7.81 - This statement is true.
2) 9 > 9 - This statement is false.
3) 8.44 > 7.81 - This statement is true.
4) 9 < 9 - This statement is false.
Therefore, the true statement is: 71 −−−√<61−−√ (start root 71 end root less than start root 61 end root).