Let’s simplify the given expression step by step:
The expression to simplify is:
[tex]\[
\sqrt{81} + \sqrt{10 - 43 - 28}
\][/tex]
### Step 1: Simplify [tex]\(\sqrt{81}\)[/tex]
First, we'll simplify the square root:
[tex]\[
\sqrt{81} = 9
\][/tex]
### Step 2: Simplify the inner expression under the second square root
Next, we'll deal with the expression inside the second square root:
[tex]\[
10 - 43 - 28
\][/tex]
Perform the subtraction inside the parentheses:
[tex]\[
10 - 43 = -33
\][/tex]
[tex]\[
-33 - 28 = -61
\][/tex]
So, the inner expression simplifies to [tex]\(-61\)[/tex].
### Step 3: Attempt to take the square root of a negative number
We now have:
[tex]\[
\sqrt{10 - 43 - 28} = \sqrt{-61}
\][/tex]
The square root of a negative number is not a real number. Since we're working under the assumption that the context is real numbers, [tex]\(\sqrt{-61}\)[/tex] is not defined in the set of real numbers. This means it's not possible to proceed in the standard arithmetic of real numbers.
### Conclusion
Since [tex]\(\sqrt{-61}\)[/tex] does not result in a real number, the expression:
[tex]\[
\sqrt{81} + \sqrt{10 - 43 - 28}
\][/tex]
does not simplify to a real number.
Thus, none of the given options ([tex]\(2, 3, 8, 1\)[/tex]) are the correct answer according to the set of real numbers. In terms of real numbers, the question as posed is not solvable and is undefined.
