Question

Using rational approximations, what statement is true? (1 point)
• the square root of 48 > the square root of 36
• the square root of 49 < 7
• the square root of 48 < the square root of 36
• the square root of 49 > 7

Answer 1

To evaluate the provided statements using rational approximations, we can analyze each one:

1. **The square root of 48 > the square root of 36**
- The square root of 36 is \(6\) (since \(6^2 = 36\)).
- The square root of 48 is approximately \(6.93\) (since \(6.93^2 \approx 48\)).
- So, \( \sqrt{48} > \sqrt{36} \) is **true**.

2. **The square root of 49 < 7**
- The square root of 49 is \(7\) (since \(7^2 = 49\)).
- So, \( \sqrt{49} < 7 \) is **false**.

3. **The square root of 48 < the square root of 36**
- Since we established that \( \sqrt{48} > \sqrt{36} \), this statement is **false**.

4. **The square root of 49 > 7**
- Since \( \sqrt{49} = 7 \), this statement is **false**.

Therefore, the only true statement is:
**The square root of 48 > the square root of 36.**