The problem is to complete a table that contains expressions written in radical notation, rational exponent notation, and their decimal approximations. We are given some entries and need to fill in the missing ones.
2025/7/3
1. Problem Description
The problem is to complete a table that contains expressions written in radical notation, rational exponent notation, and their decimal approximations. We are given some entries and need to fill in the missing ones.
2. Solution Steps
Row 2: Given in radical notation.
To convert to rational exponent form, we use the rule: .
Therefore, .
Using a calculator, .
Row 3: Given in radical notation.
To convert to rational exponent form, we use the rule: .
Therefore, .
Using a calculator, .
Row 4: Given in rational exponent notation.
To convert to radical form, we use the rule: .
Therefore, .
Using a calculator, .
Row 5: Given in rational exponent notation.
To convert to radical form, we use the rule: .
Therefore, .
Using a calculator, .
3. Final Answer
Row 2: Written using rational exponents: , Evaluated to two decimal places: 81.68
Row 3: Written using rational exponents: , Evaluated to two decimal places: 7.23
Row 4: Written in radical notation: , Evaluated to two decimal places: 23.72
Row 5: Written in radical notation: , Evaluated to two decimal places: 3.03