Certainly! Let's solve the given expression step-by-step:
The expression we need to simplify and understand is:
[tex]\[ \sqrt{22 - c} \][/tex]
1. Identify the Variables:
- The variable in this expression is [tex]\( c \)[/tex].
2. Understand the Square Root Function:
- The square root function, denoted by [tex]\( \sqrt{} \)[/tex], is a mathematical operation that returns the value which, when multiplied by itself, gives the original number.
- In this expression, we are taking the square root of [tex]\( 22 - c \)[/tex].
3. Interpret the Expression:
- Inside the square root, we have a subtraction operation, [tex]\( 22 - c \)[/tex].
- This means we are looking for the square root of the difference between 22 and [tex]\( c \)[/tex].
4. Domain Considerations:
- For the square root function to be defined, the expression inside the square root (i.e., [tex]\( 22 - c \)[/tex]) must be greater than or equal to zero.
- Therefore, [tex]\( 22 - c \geq 0 \)[/tex], which simplifies to [tex]\( c \leq 22 \)[/tex].
- Hence, [tex]\( c \)[/tex] must be less than or equal to 22 for the expression to be valid.
5. Simplifying as Much as Possible:
- The given expression [tex]\(\sqrt{22 - c}\)[/tex] is already simplified. There are no further simplifications possible without additional context or specific values for [tex]\( c \)[/tex].
6. Final Expression:
- Therefore, the final simplified form of the expression is:
[tex]\[ \sqrt{22 - c} \][/tex]
In summary, the expression [tex]\(\sqrt{22 - c}\)[/tex] represents the square root of the difference between 22 and the variable [tex]\( c \)[/tex]. For it to be defined, [tex]\( c \)[/tex] must be less than or equal to 22. The simplified form of the expression is already given as [tex]\(\sqrt{22 - c}\)[/tex].
