Which inequalities are true? Select the three correct answers.

Question

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(3 points)
Responses

0<8–√
0<8–√

8–√<3
8–√<3

8–√<2
8–√<2

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

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

Answer 1

To determine which of the inequalities are true, we will evaluate the expressions involving the square root of 8 and the square root of 7.

1. Evaluate \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \approx 2.828 \]

2. Evaluate \( \sqrt{7} \): \[ \sqrt{7} \approx 2.645 \]

Now, we can evaluate each inequality:

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

   • Since \( \sqrt{8} \) is approximately \( 2.828 \), this inequality is true.

2. Inequality: \( \sqrt{8} < 3 \)

   • Since \( \sqrt{8} \approx 2.828 \), this inequality is also true.

3. Inequality: \( \sqrt{8} < 2 \)

   • Since \( \sqrt{8} \approx 2.828 \), this inequality is false.

4. Inequality: \( \sqrt{8} > 8 \)

   • Since \( \sqrt{8} \approx 2.828 \), this inequality is false.

5. Inequality: \( \sqrt{8} > \sqrt{7} \)

   • Since \( \sqrt{8} \approx 2.828 \) and \( \sqrt{7} \approx 2.645 \), this inequality is true.

Summary of the results:

• True inequalities: \( 0 < \sqrt{8} \), \( \sqrt{8} < 3 \), and \( \sqrt{8} > \sqrt{7} \).
• False inequalities: \( \sqrt{8} < 2 \) and \( \sqrt{8} > 8 \).

Selected Correct Answers:

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

Feel free to check the answer selection as needed!