Question

Which inequalities are true? Select the four correct answers.
0 less-than StartRoot 8 EndRoot
StartRoot 8 EndRoot less-than 3
StartRoot 8 EndRoot greater-than StartRoot 7 EndRoot
StartRoot 8 EndRoot less-than 2
StartRoot 8 EndRoot greater-than 8
1 less-than StartRoot 8 EndRoot

Answer 1

To evaluate the inequalities involving \( \sqrt{8} \), we first find its approximate value:

\[
\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828
\]

Now we will check each inequality:

1. **\( 0 < \sqrt{8} \)**
True, since \( \sqrt{8} \approx 2.828 \), which is greater than 0.

2. **\( \sqrt{8} < 3 \)**
True, since \( \sqrt{8} \approx 2.828 \), which is less than 3.

3. **\( \sqrt{8} > \sqrt{7} \)**
True, since \( \sqrt{8} \approx 2.828 \) and \( \sqrt{7} \approx 2.646 \); therefore, \( 2.828 > 2.646 \).

4. **\( \sqrt{8} < 2 \)**
False, since \( \sqrt{8} \approx 2.828 \) which is greater than 2.

5. **\( \sqrt{8} > 8 \)**
False, since \( \sqrt{8} \approx 2.828 \) which is less than 8.

6. **\( 1 < \sqrt{8} \)**
True, since \( \sqrt{8} \approx 2.828 \), which is greater than 1.

Thus, the four correct inequalities are:

1. \( 0 < \sqrt{8} \)
2. \( \sqrt{8} < 3 \)
3. \( \sqrt{8} > \sqrt{7} \)
4. \( 1 < \sqrt{8} \)