Which inequalities are true? Select the three correct answers.

Question

(3 points)
Responses

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

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

0<8–√
0<8–√

8–√<2
8–√<2

8–√<3

Answer 1

To determine which inequalities are true, let's first calculate \( \sqrt{8} \):

\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \approx 2.828 \]

Now, we can analyze each inequality:

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

   • True. Since \( 8 > 7 \), it follows that \( \sqrt{8} > \sqrt{7} \).

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

   • False. \( 2.828 < 8 \).

3. \( 0 < \sqrt{8} \)

   • True. Since \( \sqrt{8} \) is a positive number.

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

   • False. Since \( 2.828 > 2 \).

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

   • True. Since \( 2.828 < 3 \).

Now we summarize the truth values:

• True: \( \sqrt{8} > \sqrt{7} \) (first response), \( 0 < \sqrt{8} \) (third response), and \( \sqrt{8} < 3 \) (fifth response).
• False: \( \sqrt{8} > 8 \) (second response) and \( \sqrt{8} < 2 \) (fourth response).

The correct answers are:

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