Hey Bot, using rational approximations, what statement is true?(1 point)
Responses
49−−√<7
48−−√<36−−√
48−−√>36−−√
49−−√>7
The statement that is true is 49−−√>7.
To determine which statement is true using rational approximations, we need to convert the given square root expressions into decimal approximations.
1. Evaluating 49−−√:
√49 = 7 since 7^2 = 49
So, the decimal approximation of 49−−√ is 7.
2. Evaluating 48−−√:
To approximate the square root of 48, we can find the perfect square closest to 48, which is 49.
√49 = 7
So, the decimal approximation of 48−−√ is approximately 7.
3. Evaluating 36−−√:
√36 = 6 since 6^2 = 36
So, the decimal approximation of 36−−√ is 6.
From the above approximations, we can compare the statements:
a) 49−−√ < 7: This statement is false because 49−−√ equals 7.
b) 48−−√ < 36−−√: This statement is true because the decimal approximations show that 48−−√ is approximately 7, which is greater than 6.
c) 48−−√ > 36−−√: This statement is true because the decimal approximations show that 48−−√ is approximately 7, which is indeed greater than 6.
d) 49−−√ > 7: This statement is false because 49−−√ equals 7.
Therefore, the true statement is either b) 48−−√ < 36−−√ or c) 48−−√ > 36−−√.