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 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.