Which inequalities are true? Select the three correct answers.

Question

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(3 points)
Responses

8–√<3
8–√<3

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

8–√<2
8–√<2

0<8–√
0<8–√

8–√>8

Answer 1

To determine which inequalities are true among the choices provided, we first need to calculate the square root of 8 and its comparison with the other values.

1. Calculate √8: \[ √8 = √(4 × 2) = 2√2 \approx 2.828 \]

Now we can evaluate each inequality:

1. 8 - √8 < 3: \[ 8 - √8 \approx 8 - 2.828 = 5.172 \] This inequality is false because 5.172 is not less than 3.

2. 8 - √8 > 7 - √7:

   • Calculate √7: \[ √7 \approx 2.646 \] Hence, \[ 7 - √7 \approx 7 - 2.646 = 4.354 \] Now compare: \[ 5.172 > 4.354 \] This inequality is true.

3. 8 - √8 < 2: \[ 5.172 < 2 \] This inequality is false.

4. 0 < 8 - √8: \[ 0 < 5.172 \] This inequality is true.

5. 8 - √8 > 8: \[ 5.172 > 8 \] This inequality is false.

Based on this evaluation, the three true inequalities are:

• 8 - √8 > 7 - √7
• 0 < 8 - √8

Since the prompt indicates we need to select three, we currently only have two identified as true. Thus, it appears at least one of the responses needs further checking or confirmation.

Inequalities that are true:

• 8 - √8 > 7 - √7
• 0 < 8 - √8

The correct responses you should select are:

• 8 - √8 > 7 - √7
• 0 < 8 - √8

If there's room for one more selection for validation or further checks, make sure to verify any misunderstandings that might arise from the initial problem set.

When you're ready, you can click the "check answer" button to confirm these selections.