Using rational approximations, what statement is true?(1 point)
Responses
48−−√>36−−√
start root 48 end root greater than start root 36 end root
49−−√>7
start root 49 end root greater than 7
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√<7
start root 49 end root less than 7
start root 49 end root less than 7
To determine which statement is true using rational approximations, we can simplify the square roots to their nearest rational numbers.
1. √48 is approximately equal to √49, since 49 is the nearest perfect square to 48. Therefore, √48 ≈ √49 = 7.
2. √36 is equal to 6, and 7 is greater than 6. So, √48 is greater than √36.
Therefore, the true statement is:
48−−√ > 36−−√