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

Question

Responses

8–√<5
8–√<5

6–√<2
6–√<2

0<4–√
0<4–√

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

8–√>6–√

Answer 1

To evaluate the inequalities, let's calculate the square roots involved:

1. \( \sqrt{8} \) is approximately \( 2.83 \) (since \( 2.83^2 \approx 8 \)).
2. \( \sqrt{6} \) is approximately \( 2.45 \) (since \( 2.45^2 \approx 6 \)).
3. \( \sqrt{4} = 2 \).

Now, let's examine each inequality:

1. \( 8 - \sqrt{8} < 5 \): \[ 8 - 2.83 \approx 5.17 < 5 \quad \text{(False)} \]

2. \( 6 - \sqrt{6} < 2 \): \[ 6 - 2.45 \approx 3.55 < 2 \quad \text{(False)} \]

3. \( 0 < 4 - \sqrt{4} \): \[ 0 < 4 - 2 = 2 \quad \text{(True)} \]

4. \( \sqrt{8} > 3 \): \[ 2.83 > 3 \quad \text{(False)} \]

5. \( \sqrt{8} > \sqrt{6} \): \[ 2.83 > 2.45 \quad \text{(True)} \]

Based on the analysis, the true inequalities are:

• \( 0 < 4 - \sqrt{4} \)
• \( \sqrt{8} > \sqrt{6} \)

However, please note that we only found two true inequalities based on the calculations provided. Therefore, if selecting three answers is mandatory, it seems that it would not be possible with the options available.