Question

using rational approximations, what statement is true

√71 < √61
√81 > 9
√71 < √61
√81 < 9

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct statement is:

√71 < √61

Answer 2

[AI-generated answer — Step-by-Step Bot]

The statement that is true is: √81 > 9.

By rational approximations, we can simplify the square roots to whole numbers to compare them accurately.

√71 is not a perfect square, so we can use rational approximations to estimate. The square root of 71 is approximately 8.4.

√61 is also not a perfect square, so we can use rational approximations to estimate. The square root of 61 is approximately 7.8.

Therefore, √71 < √61 is not true.

√81 is a perfect square, and the actual value is 9.

Since 9 is a smaller number than √81, the statement √81 < 9 is also not true.

Therefore, the only true statement using rational approximations is: √81 > 9.