Which inequalities are true? Select the three correct answers.

Question

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(3 points)
Responses

8–√<2
8–√<2

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

8–√<3
8–√<3

0<8–√
0<8–√

8–√>8

Answer 1

Let's evaluate each inequality one by one:

1. 8 - √ < 2

   • This suggests: 8 - √ < 2.
   • Rearranging gives: 8 - 2 < √, or √ > 6.
   • This is incorrect since the square root of any number is non-negative, and there is no real number whose square root is greater than 6.

2. 8 - √ > 7 - √

   • This suggests: 8 - √ > 7 - √.
   • Rearranging gives: 8 > 7, which is true.
   • Therefore, this inequality is correct.

3. 8 - √ < 3

   • This suggests: 8 - √ < 3.
   • Rearranging gives: 8 - 3 < √, or 5 < √.
   • This is incorrect, as the square root of a positive number (in this case, √) cannot be less than 5.

4. 0 < 8 - √

   • This suggests: 0 < 8 - √.
   • Rearranging gives: √ < 8, which is always true for real numbers.
   • Therefore, this inequality is correct.

5. 8 - √ > 8

   • This suggests: 8 - √ > 8.
   • Rearranging gives: -√ > 0.
   • This is false because the square root is always non-negative.

So the correct inequalities are:

• 8 - √ > 7 - √
• 0 < 8 - √

Thus, the three correct inequalities should be selected as:

1. 8 - √ > 7 - √
2. 0 < 8 - √
3. You would need to select one additional option, but there are only these two valid inequalities, so the third option does not exist among the provided responses.

Please select the two valid inequalities indicated above. If you need to select three answers as requested, then there might be a mistake in the options provided.