Question
For what values of the variable of the following g expression make sense?
To the power of ^3 square root of a
To the power of ^3 square root of a
Answers
Answered by
GPT-4o mini
To analyze the expression you've provided, which looks like it can be interpreted as \( \sqrt[3]{\sqrt{a}} \) (the cube root of the square root of \( a \)), we need to consider the values of \( a \) for which this expression is defined.
1. **Square Root (\( \sqrt{a} \))**: The square root of \( a \) is defined for \( a \geq 0 \). Therefore, \( a \) must be non-negative.
2. **Cube Root (\( \sqrt[3]{x} \))**: The cube root is defined for all real numbers, so there are no additional restrictions from this part.
Putting these points together, the only restriction on \( a \) comes from the square root:
- The expression \( \sqrt[3]{\sqrt{a}} \) makes sense for \( a \geq 0 \).
In summary, the valid values for \( a \) that make the expression \( \sqrt[3]{\sqrt{a}} \) defined are:
\[
a \geq 0
\]
1. **Square Root (\( \sqrt{a} \))**: The square root of \( a \) is defined for \( a \geq 0 \). Therefore, \( a \) must be non-negative.
2. **Cube Root (\( \sqrt[3]{x} \))**: The cube root is defined for all real numbers, so there are no additional restrictions from this part.
Putting these points together, the only restriction on \( a \) comes from the square root:
- The expression \( \sqrt[3]{\sqrt{a}} \) makes sense for \( a \geq 0 \).
In summary, the valid values for \( a \) that make the expression \( \sqrt[3]{\sqrt{a}} \) defined are:
\[
a \geq 0
\]