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

Question

Responses

6–√<2
6√<2

8√<5
8–√<5

0<4–√
0<4–√

8–√>6–√
square root of 8 is greater than square root of 6

8√>3

Answer 1

To determine which inequalities are true, let's evaluate each one step by step.

1. 6 - √ < 2:

   • Approximate √ (square root of 6) ≈ 2.45, so 6 - 2.45 ≈ 3.55.
   • Thus, 3.55 < 2 is false.

2. 6√ < 2:

   • This is generally interpreted as \(6 \times \sqrt{}\), and since \(6\) multiplied by any positive number is greater than \(2\), this is false.

3. 8√ < 5:

   • Again, assuming this is \(8 \times \sqrt{}\), \(8\) multiplied by any positive number will also be greater than \(5\), so this is false.

4. 8 - √ < 5:

   • Approximate √ (square root of 8) ≈ 2.83, so 8 - 2.83 ≈ 5.17, thus 5.17 < 5 is false.

5. 0 < 4 - √:

   • Assuming √ refers to \(√4\) or simply \(2\), we have \(4 - 2 = 2\). Since \(0 < 2\), this is true.

6. 8 - √ > 6 - √:

   • Approximate √ (square root of 8) ≈ 2.83 and √ (square root of 6) ≈ 2.45
   • Then 8 - 2.83 = 5.17 and 6 - 2.45 = 3.55, so 5.17 > 3.55 is true.

7. 8√ > 3:

   • Assuming this means \(8 \times \sqrt{}\), and since \(8\) is a positive number, this is generally true for positive values under the square root.

Therefore, the three correct answers are:

• 0 < 4 - √
• 8 - √ > 6 - √
• 8√ > 3