Using rational approximations, what statement is true?
Responses
71 −−−√<61−−√
71 −−−√<61−−√
- no response given
81−−√>9
71−−√>61−−√
81−−√<9
The statement "81√>9" is true.
The correct statement using rational approximations is:
71 - √< 61 - √
To determine the true statement using rational approximations, we need to compare the given expressions and determine the relationship between them.
Let's simplify the expressions first:
For the first expression, 71 −−√<61−−√:
To compare the square roots, we can approximate them. The square root of 71 is approximately 8.44, and the square root of 61 is approximately 7.81. Comparing these values, 8.44 is indeed greater than 7.81. Therefore, the first expression is true: 71 −−√<61−−√.
For the second expression, 81−−√>9:
Again, let's approximate the square roots. The square root of 81 is 9, and 9 is indeed greater than 9. Therefore, the second expression is true: 81−−√>9.
For the third expression, 71−−√>61−−√:
Using the same approximations as before, the square root of 71 is approximately 8.44, and the square root of 61 is approximately 7.81. We can see that 8.44 is indeed greater than 7.81. Therefore, the third expression is true: 71−−√>61−−√.
Lastly, for the fourth expression, 81−−√<9:
Again, let's approximate the square roots. The square root of 81 is 9, and 9 is not less than 9. Therefore, the fourth expression is false: 81−−√<9.
In conclusion, the true statements using rational approximations are:
1. 71 −−√<61−−√
2. 81−−√>9
3. 71−−√>61−−√