Using rational approximations, what statement is true?(1 point)
Responses
√81 > 9
√71 < √61
√81 < 9
√71 > √61
no, √81 = 9
√71 > √61
Apologies for the confusion. You are correct. The statement √71 > √61 is true.
The correct statement using rational approximations is: √71 < √61.
To determine the truth of the statements involving square roots (√), we can simplify the square roots using rational approximations.
First, let's simplify √81:
Since 9^2 = 81, the square root of 81 is 9.
Now, let's compare √81 and 9:
√81 = 9
9 is equal to 9, so the statement √81 = 9 is true.
Next, let's simplify √71 and √61:
We need to find rational approximations for √71 and √61.
By using a calculator or estimation techniques, we can determine that:
√71 ≈ 8.4261
√61 ≈ 7.8102
Now, let's compare √71 and √61:
√71 ≈ 8.4261
√61 ≈ 7.8102
8.4261 is greater than 7.8102, so the statement √71 > √61 is true.
To summarize, the true statement among the options given is:
√71 > √61