Using rational approximations, what statement is true?(1 point)

Question

Responses

48−−√>36−−√
start root 48 end root greater than start root 36 end root

48−−√<36−−√
start root 48 end root less than start root 36 end root

49−−√>7
start root 49 end root greater than 7

49−−√<7
start root 49 end root less than 7

Answer 1

To analyze the statements, we need to calculate the values of the square roots:

1. √48 > √36:

   • √36 = 6
   • To compare √48 to 6, we can approximate √48. We know that √49 = 7 (since 49 is a perfect square) and √36 = 6. Therefore, √48 is between 6 and 7, but closer to 7.
   • Since √48 is not clearly greater than zero, we check: 48 < 49 (but greater than 36). Thus, we cannot definitively claim √48 > √36.

2. √48 < √36:

   • As established before, √36 = 6, and √48 is greater than √36, since 48 is greater than 36. So, this statement is false.

3. √49 > 7:

   • √49 = 7. Therefore, this statement is false.

4. √49 < 7:

   • Again, since √49 = 7, this statement is false.

Thus, the true statement among the given options is: √48 > √36.