Question

Using rational approximations what statement is true?


A: √49 < 7

B: √49 > 7

C: √48 < √36

D: √48 > √36

Answer 1

using rational approximation what statement is true

A: √81 > 9

B: √81 < 9

C: √71 > √61

D: √71 < √61

Answer 2

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 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.**