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

Question

Responses

6–√<2
6–√<2

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

0<4–√
0<4–√

8–√<5
8–√<5

8–√>3

Answer 1

To determine which inequalities are true, we'll evaluate each one:

1. \( 6 - \sqrt{2} < 2 \):

   • Calculating \( \sqrt{2} \) gives approximately 1.414.
   • Therefore, \( 6 - \sqrt{2} \approx 6 - 1.414 \approx 4.586 \).
   • Since \( 4.586 < 2 \) is false, this inequality is not true.

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

   • Calculating \( \sqrt{8} \approx 2.828 \) and \( \sqrt{6} \approx 2.449 \).
   • Since \( 2.828 > 2.449 \) is true, this inequality is true.

3. \( 0 < \sqrt{4} \):

   • Since \( \sqrt{4} = 2 \), the inequality \( 0 < 2 \) is true. Thus, this inequality is true.

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

   • We've already calculated \( \sqrt{8} \approx 2.828 \).
   • Since \( 2.828 < 5 \) is true, this inequality is true.

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

   • We know \( \sqrt{8} \approx 2.828 \) and since \( 2.828 \) is not greater than \( 3 \), this inequality is not true.

The three correct inequalities are:

1. \( \sqrt{8} > \sqrt{6} \)
2. \( 0 < \sqrt{4} \)
3. \( \sqrt{8} < 5 \)