Question

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 less than 7 48−−√<36−−√ start root 48 end root less than start root 36 end root 49−−√>7

Answer 1

To determine which of the statements is true using rational approximations, we can evaluate the square roots involved.

1. Evaluate √48 and √36:

   • √36 = 6 (exact)
   • √48 can be approximated as:
     • √48 = √(16 * 3) = 4√3
     • Since √3 is approximately 1.732, then:
     • 4√3 ≈ 4 * 1.732 ≈ 6.928

   Therefore, √48 ≈ 6.928, and we have:

   • √48 > √36 (6.928 > 6).

2. Evaluate √49:

   • √49 = 7 (exact).

Now, we compare √49 with 7:

• √49 = 7

3. We can summarize:
   • √48 > √36 (True)
   • √49 < 7 (False, √49 = 7)
   • √48 < √36 (False)
   • √49 > 7 (False)

Thus, the only true statement is:

√48 > √36.