Using rational approximations what statement is true
√71 > √61
√71 < √61
√81 < 9
√81 > 9
The correct statement is:
√71 > √61
To determine which statement is true using rational approximations, let's calculate the decimal approximations for each side of the inequalities.
1. √71 ≈ 8.4 (approximation to one decimal place)
√61 ≈ 7.8 (approximation to one decimal place)
Therefore, √71 > √61 is true because 8.4 is greater than 7.8.
2. √81 = 9 (exact square root)
Therefore, √81 = 9 is true because the square root of 81 is exactly 9.
Based on the rational approximations, the true statements are:
- √71 > √61
- √81 = 9
Therefore, the correct statements are √71 > √61 and √81 > 9.