Using rational approximations what statement is true?

Question

A: √49 < 7

B: √49 > 7

C: √48 < √36

D: √48 > √36

Answer 1

To evaluate the statements using rational approximations:

1. A: √49 < 7

   • This is false because √49 = 7.

2. B: √49 > 7

   • This is also false because √49 = 7.

3. C: √48 < √36

   • Calculating these, √48 is approximately 6.93, and √36 = 6. Thus, this statement is false because 6.93 > 6.

4. D: √48 > √36

   • As established, √48 ≈ 6.93 and √36 = 6. Hence, this statement is true because 6.93 > 6.

Therefore, the correct statement is:

D: √48 > √36.

Answer 2

using rational approximation what statement is true

A: √81 > 9

B: √81 < 9

C: √71 > √61

D: √71 < √61

Answer 3

Let's evaluate each statement using rational approximations:

1. A: √81 > 9

   • This is false because √81 = 9.

2. B: √81 < 9

   • This is also false because √81 = 9.

3. C: √71 > √61

   • Approximating the square roots:
     • √71 is approximately 8.43.
     • √61 is approximately 7.81.
   • This statement is true because 8.43 > 7.81.

4. D: √71 < √61

   • This is false as established because 8.43 is not less than 7.81.

The correct statement is:

C: √71 > √61.