Which inequalities are true? Select the three correct answers.(3 points)

Question

Responses

8–√>6–√
square root of 8 is greater than square root of 6

8–√>3
square root of 8 is greater than 3

8–√<5
8–√<5

6–√<2
6–√<2

0<4–√

Answer 1

To evaluate the inequalities involving square roots, we can calculate the approximate values of the square roots:

1. \(\sqrt{8} \approx 2.83\)
2. \(\sqrt{6} \approx 2.45\)
3. \(\sqrt{5} \approx 2.24\)
4. \(\sqrt{4} = 2\)

Now, let's analyze each statement:

1. \(\sqrt{8} > \sqrt{6}\):

   • True, because \(2.83 > 2.45\).

2. \(\sqrt{8} > 3\):

   • False, because \(2.83 < 3\).

3. \(\sqrt{8} < 5\):

   • True, because \(2.83 < 5\).

4. \(\sqrt{6} < 2\):

   • False, because \(2.45 > 2\).

5. \(0 < \sqrt{4}\):

   • True, because \(\sqrt{4} = 2\), which is greater than 0.

Therefore, the correct true inequalities are:

• \(\sqrt{8} > \sqrt{6}\)
• \(\sqrt{8} < 5\)
• \(0 < \sqrt{4}\)

The three correct answers are:

• \(8–\sqrt{,} > 6–\sqrt{,}\)
• \(8–\sqrt{,} < 5\)
• \(0 < 4–\sqrt{,}\)