Answer:
-n
Explanation:
The symbol √ means the principal square root.
The principal square root is always non-negative.
For example, even though the number 25 has two square roots, -5 and 5, since both (-5)² and (5)² equal 25, when you express the square root using the square root symbol, then √25 = 5, and not -5, since √25 means the principal square root of 25, and as a principal square root, it must be a non-negative number.
If n < 0, then you are dealing with negative numbers.
Once you square n to get n², n² is a positive number.
Then the square root of n², expressed with the square root symbol as √(n²) must be positive, so it equals -n.
Example:
Let n = -8.
Then n² = (-8)² = 64.
√(64) = 8
Compare 8 to -8. 8 is -(-8), just like we get -n.
Answer: -n