Solve the following question:

6. What is the number obtained when simplifying the expression:

[tex]\[ \sqrt{81} + \sqrt{10 - 43 + 28} \][/tex]

A) 2
B) 3
C) 8
D) 1
E) 4



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.