plot 3 - √2 and 3^√2 on the decimal number line.

Question

Based on your answer above, compare and using <, >, or =.

3^√2 and 3 -√2

Answer 1

To plot 3 - √2 and 3^√2 on the decimal number line, we first need to approximate their values:

3 - √2 ≈ 3 - 1.414 ≈ 1.586
3^√2 ≈ 3^1.414 ≈ 3^1.414 ≈ 3^1.414 ≈ 3^1.414 ≈ 3^1.414 ≈ 3.16

Now, on the decimal number line:
- 3 - √2 ≈ 1.586
- 3^√2 ≈ 3.16

1.586 < 3.16

Therefore, 3 - √2 is less than 3^√2, which can be represented as 3 - √2 < 3^√2.