To solve these problems, let's evaluate each expression in turn:
### Evaluating [tex]\(\sqrt{-49}\)[/tex]:
1. The expression [tex]\(\sqrt{-49}\)[/tex] asks for the square root of [tex]\(-49\)[/tex].
2. In the set of real numbers, taking the square root of a negative number is not possible. The square root is defined only for non-negative values.
3. Therefore, the square root of [tex]\(-49\)[/tex] is not a real number.
Hence, [tex]\(\sqrt{-49}\)[/tex] is Not a real number.
### Evaluating [tex]\(-\sqrt{25}\)[/tex]:
1. First, we find the square root of 25. The square root of 25 is the number that, when multiplied by itself, gives 25.
2. That number is 5 because [tex]\(5 \times 5 = 25\)[/tex].
3. Next, we take the negative of this value, which is [tex]\(-5\)[/tex].
So, [tex]\(-\sqrt{25} = -5\)[/tex].
### Final Answer
[tex]\[
\begin{array}{l}
\sqrt{-49}= \text{Not a real number} \\
-\sqrt{25}= -5
\end{array}
\][/tex]
You would click "Not a real number" for [tex]\(\sqrt{-49}\)[/tex] and replace the square with [tex]\(-5\)[/tex] for [tex]\(-\sqrt{25}\)[/tex].
