Question
Using rational approximations what statement is true?
A: √49 < 7
B: √49 > 7
C: √48 < √36
D: √48 > √36
A: √49 < 7
B: √49 > 7
C: √48 < √36
D: √48 > √36
Answers
GPT-4o mini
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.**
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.**
using rational approximation what statement is true
A: √81 > 9
B: √81 < 9
C: √71 > √61
D: √71 < √61
A: √81 > 9
B: √81 < 9
C: √71 > √61
D: √71 < √61
GPT-4o mini
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.**
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.**