plot 3 -√2 and 3^√2 on the decimal number line.
Based on your answer above, compare and using <, >, or =.
3 -√2 and 3^√2
To plot 3 - √2 on the decimal number line, we can approximate the value by using a calculator.
3 - √2 ≈ 3 - 1.4142 ≈ 1.5858
Therefore, 3 - √2 ≈ 1.5858
To plot 3^√2 on the decimal number line, we can calculate the value by raising 3 to the power of √2.
3^√2 = 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142 ≈ 3^1.4142
Therefore, 3^√2 ≈ 3^1.4142 ≈ 3.0831
Now, we can plot these values on the number line:
1.5858-----------------------------------------------3.0831
Comparing the two values:
1.5858 < 3.0831
Therefore, 3-√2 < 3^√2.