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

8–√<5

Answer 1

Let’s evaluate each inequality one by one:

1. 6–√ < 2

   • \( \sqrt{6} \) is approximately 2.45, so \( 6 - \sqrt{6} \approx 6 - 2.45 = 3.55 \).
   • Thus, \( 6 - \sqrt{6} < 2 \) is false.

2. 8–√ > 6–√

   • \( \sqrt{8} \) is approximately 2.83, and \( \sqrt{6} \) is approximately 2.45.
   • Thus, \( \sqrt{8} > \sqrt{6} \) is true.

3. 0 < 4–√

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

4. 8–√ > 3

   • We've deemed \( \sqrt{8} \approx 2.83 \), which is not greater than 3. Thus, this statement is false.

5. 8–√ < 5

   • Since \( \sqrt{8} \approx 2.83 \), \( 2.83 < 5 \) is true.

Based on this evaluation, the correct inequalities are:

• 8–√ > 6–√
• 0 < 4–√
• 8–√ < 5

So, the three correct answers are:

• 8–√ > 6–√
• 0 < 4–√
• 8–√ < 5