plot 3 - √2 and \sqrt[3]{2} on the decimal number line.

Question

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

\sqrt[3]{2} and 3 - √2

Answer 1

To plot √2 and \sqrt[3]{2} on the decimal number line, we need to approximate their decimal values.

√2 is approximately 1.414
\sqrt[3]{2} is approximately 1.260

Now, let's compare:
1.260 < 1.414

Therefore, \sqrt[3]{2} is less than √2.

Now, let's compare \sqrt[3]{2} and 3 - √2:
\sqrt[3]{2} = 1.260
3 - √2 ≈ 1

Therefore, \sqrt[3]{2} is greater than 3 - √2.