Which inequalities are true? Select the three correct answers.

Question

(3 points)
Responses

0<8–√
0<8–√

8–√<2
8–√<2

8–√<3
8–√<3

8–√>7–√
square root of 8 is greater than square root of 7

8–√>8

Answer 1

To determine which inequalities are true, let's first calculate the values involved:

1. Calculate \(\sqrt{8}\) and compare it to the other values.

   • \(\sqrt{8} \approx 2.828\)

2. Calculate \(\sqrt{7}\).

   • \(\sqrt{7} \approx 2.646\)

Now we can evaluate the inequalities:

1. \(0 < \sqrt{8}\)

   • This is true, as \(\sqrt{8} \approx 2.828\), which is greater than 0.

2. \(\sqrt{8} < 2\)

   • False, since \(\sqrt{8} \approx 2.828\), which is not less than 2.

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

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

4. \(\sqrt{8} > \sqrt{7}\)

   • True, since \(\sqrt{8} \approx 2.828\) and \(\sqrt{7} \approx 2.646\), meaning \(\sqrt{8}\) is greater than \(\sqrt{7}\).

5. \(\sqrt{8} > 8\)

   • False, since \(\sqrt{8} \approx 2.828\), which is not greater than 8.

Now we can summarize the valid inequalities:

• True: \(0 < \sqrt{8}\)
• True: \(\sqrt{8} < 3\)
• True: \(\sqrt{8} > \sqrt{7}\)

The three correct answers are:

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