Question

Which inequalities are true? Select the three correct answers.

A. \sqrt(6) < 2
B. \sqrt(8) > 3
C. \sqrt(8) < 5
D. \sqrt(8) > \sqrt(6)
E. 0 < \sqrt(4)

Answer 1

To determine which inequalities are true, let's evaluate each option:

A. \(\sqrt{6} < 2\)
- Since \(\sqrt{4} = 2\) and \(\sqrt{6} \approx 2.45\), this inequality is false.

B. \(\sqrt{8} > 3\)
- \(\sqrt{8} \approx 2.83\), which is not greater than 3. Therefore, this inequality is false.

C. \(\sqrt{8} < 5\)
- Since \(\sqrt{8} \approx 2.83\), this inequality is true.

D. \(\sqrt{8} > \sqrt{6}\)
- We have \(\sqrt{8} \approx 2.83\) and \(\sqrt{6} \approx 2.45\). Since \(2.83 > 2.45\), this inequality is true.

E. \(0 < \sqrt{4}\)
- \(\sqrt{4} = 2\), thus \(0 < 2\) is true.

The three correct inequalities are:
- C. \(\sqrt{8} < 5\)
- D. \(\sqrt{8} > \sqrt{6}\)
- E. \(0 < \sqrt{4}\)