Using rational approximations, what statement is true?(1 point)
Responses
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
71−−√>61−−√
start root 71 end root greater than start root 61 end root
81−−√<9
start root 81 end root less than 9
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 greater 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 is less than pi
who needs you
its start root 70 is greater than 61
71****
To determine which statement is true using rational approximations, we need to approximate the square roots involved.
Let's start by approximating √71. We can find rational approximations by looking for perfect squares that are close to 71. The perfect square closest to 71 is 64 (8^2), and the perfect square larger than 71 is 81 (9^2). So, we can approximate √71 as a number between 8 and 9.
Next, let's approximate √61. The perfect square closest to 61 is 49 (7^2), and the perfect square larger than 61 is 64 (8^2). So, we can approximate √61 as a number between 7 and 8.
Comparing the two approximations, √71 is larger than √61 because 8 is greater than 7. Therefore, the first statement (71−−√<61−−√) is not true.
Now, let's evaluate the second statement (71−−√>61−−√). Since we have already established that √71 is larger than √61, we can conclude that the second statement is true.
The last two statements involve square roots being compared to a perfect square. Let's evaluate them:
√81 is equal to 9, and we can clearly see that 9 is not less than 9. Therefore, the third statement (81−−√<9) is not true.
Similarly, √81 is equal to 9, and we can clearly see that 9 is not greater than 9. Therefore, the fourth statement (81−−√>9) is not true.
To summarize, the second statement (71−−√>61−−√) is the only true statement among the given options.