Я уже просто не понимаю, что не так...
#include <iostream>
#include <iomanip>
using namespace std;
int main() {
    long double arr[100000];
    for (int x = 0; x<100000; x++) {
        cin >> arr[x];
    }
    for (int y = 100000; y--;) {
        arr[y] = sqrt(arr[y]);
        cout << fixed << setprecision(4) << (arr[y]) << endl;
    }
    return 0;
}

How did you receive a magic number "100000"?

Task example, for example, contains 4 numbers. Your program should process example.

My program processes the example of 4 digits, but still wrong answer

> My program
Which one? From the topic start post? It isn't. Please look at
https://ideone.com/AhvmV1

No.This https://ideone.com/wdz80E.

Could you read task description? It should help a bit.

Amount of numbers in the input isn't fixed. You should read numbers from input until EOF.
By task description maximum input size IN BYTES is 256Kb. You should estimate maximum input size in numbers yourself.