Answer :
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.
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.
