Using rational approximations, what statement is true? (1 point)
sqrt(48) > sqrt(36)
sqrt(49) > 7
sqrt(48) < sqrt(36)
sqrt(49) < 7
The statement that is true using rational approximations is:
sqrt(49) < 7.
To determine which statement is true using rational approximations, we need to evaluate the square roots using the nearest perfect squares.
Let's compare the statements:
Statement 1: sqrt(48) > sqrt(36)
The nearest perfect squares are 49 (7^2) and 36 (6^2).
sqrt(49) is greater than sqrt(36), so Statement 1 is true.
Statement 2: sqrt(49) > 7
The square root of 49 is exactly 7, so sqrt(49) is not greater than 7. Therefore, Statement 2 is false.
Statement 3: sqrt(48) < sqrt(36)
Again, using the nearest perfect squares, we can see that sqrt(48) is less than sqrt(36). Therefore, Statement 3 is true.
Statement 4: sqrt(49) < 7
Since sqrt(49) is exactly 7, it is not less than 7. Thus, Statement 4 is false.
In conclusion, the true statements are:
Statement 1: sqrt(48) > sqrt(36)
Statement 3: sqrt(48) < sqrt(36)
Note: We can also calculate the exact values of the square roots using a calculator or long division method, but rational approximations provide a quick way to compare the statements.