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

Question

Responses

6–√<2
6–√<2

0<4–√
0<4–√

8–√<5
8–√<5

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

8–√>6–√

Answer 1

To determine which of the inequalities are true, let's evaluate each one step by step.

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

   • First, calculate \( \sqrt{2} \) which is approximately \( 1.414 \).
   • Therefore, \( 6 - \sqrt{2} \approx 6 - 1.414 = 4.586 \).
   • \( 4.586 < 2 \) is false.

2. \( 0 < 4 - \sqrt{4} \)

   • Calculate \( \sqrt{4} = 2 \).
   • Therefore, \( 4 - \sqrt{4} = 4 - 2 = 2 \).
   • \( 0 < 2 \) is true.

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

   • Calculate \( \sqrt{8} \) which is approximately \( 2.828 \).
   • \( 2.828 < 5 \) is true.

4. \( \sqrt{8} > 3 \)

   • We already found \( \sqrt{8} \approx 2.828 \).
   • \( 2.828 > 3 \) is false.

5. \( \sqrt{8} > \sqrt{6} \)

   • Calculate \( \sqrt{6} \) which is approximately \( 2.449 \).
   • Since \( 2.828 > 2.449 \), this is true.

Based on the evaluations above, the three correct true inequalities are:

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

Therefore, the true inequalities are the second, third, and fifth responses.