Question

Using rational approximations, what statement is true?

options:

√48 > √36

√49 < 7

√49 > 7

√48 < √36

Answer 1

To analyze the statements provided using rational approximations, let's evaluate the values of the square roots:

1. **√48**: We know that \( \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \). Approximating \( \sqrt{3} \approx 1.732 \), we have:
\[
\sqrt{48} \approx 4 \times 1.732 = 6.928
\]

2. **√36**: This is straightforward, as \( \sqrt{36} = 6 \).

3. **√49**: This is also straightforward, as \( \sqrt{49} = 7 \).

Now let's evaluate the options:

1. **√48 > √36**
- We have \( \sqrt{48} \approx 6.928 \) and \( \sqrt{36} = 6 \). So, this statement is true.

2. **√49 < 7**
- Since \( \sqrt{49} = 7 \), this statement is false.

3. **√49 > 7**
- Also false, because \( \sqrt{49} = 7 \).

4. **√48 < √36**
- False, as we determined \( \sqrt{48} \approx 6.928 > 6 \).

The only true statement is:

**√48 > √36**.