Let's evaluate the given expressions step-by-step:
1. Square root of -9:
- To find the square root of a number, we are typically looking for a value that can be multiplied by itself to give the original number.
- In this case, we are trying to find a number such that when squared, it equals -9.
- However, within the realm of real numbers, no real number squared will result in a negative value because the multiplication of two positive numbers or two negative numbers always results in a positive number.
- Therefore, taking the square root of a negative number does not yield a real number result.
- Hence, the square root of -9 is Not a real number.
Now, let's move to the next expression:
2. Negative square root of 1:
- Here, we are first considering the square root of 1.
- The square root of 1 is 1 because [tex]\(1^2 = 1\)[/tex].
- Since we are asked for the negative square root, we take the negative of the square root of 1.
- Therefore, the negative square root of 1 is [tex]\(-1\)[/tex].
So, the detailed evaluations and answers for the given expressions are:
1. [tex]\(\sqrt{-9}\)[/tex] : Not a real number
2. [tex]\(-\sqrt{1}\)[/tex] : [tex]\(-1\)[/tex]
