RMSE using mean_squared_error does not return the correct value

### Describe the bug

The RMSE value obtained from mean_squared_error function with the squared parameter set to false return a different value compared to manually root the MSE obtained by the same function

### Steps/Code to Reproduce

```shell
from sklearn.metrics import mean_squared_error
import numpy as np
import math

# calculate All Relevant Metric
rmse = mean_squared_error(testy, ypred, squared=False)
mse = mean_squared_error(testy, ypred)
rmse2 = np.sqrt(mse)
rmse3 = math.sqrt(mse)

#Print All The Result
print(mse)
print(rmse)
print(rmse2)
print(rmse3)
```

### Expected Results

37384.461953883205
193.3506192229112
193.3506192229112
193.3506192229112

### Actual Results

37384.461953883205
78.94719343148691
193.3506192229112
193.3506192229112

### Versions

```shell
System:
    python: 3.9.12 (tags/v3.9.12:b28265d, Mar 23 2022, 23:52:46) [MSC v.1929 64 bit (AMD64)]
executable: c:\Users\SRI-LAB-05\AppData\Local\Programs\Python\Python39\python.exe
   machine: Windows-10-10.0.22621-SP0

Python dependencies:
      sklearn: 1.2.0
          pip: 22.3.1
   setuptools: 58.1.0
        numpy: 1.24.1
        scipy: 1.9.3
       Cython: None
       pandas: 1.5.2
   matplotlib: 3.6.2
       joblib: 1.2.0
threadpoolctl: 3.1.0

Built with OpenMP: True

threadpoolctl info:
       user_api: openmp
   internal_api: openmp
         prefix: vcomp
       filepath: C:\Users\SRI-LAB-05\AppData\Local\Programs\Python\Python39\Lib\site-packages\sklearn\.libs\vcomp140.dll
        version: None
    num_threads: 20

       user_api: blas
   internal_api: openblas
         prefix: libopenblas
       filepath: C:\Users\SRI-LAB-05\AppData\Local\Programs\Python\Python39\Lib\site-packages\numpy\.libs\libopenblas64__v0.3.21-gcc_10_3_0.dll
        version: 0.3.21
threading_layer: pthreads
   architecture: Haswell
    num_threads: 20

       user_api: blas
   internal_api: openblas
         prefix: libopenblas
       filepath: C:\Users\SRI-LAB-05\AppData\Local\Programs\Python\Python39\Lib\site-packages\scipy.libs\libopenblas-57db09cfe174768fb409a6bb5a530d4c.dll
        version: 0.3.18
threading_layer: pthreads
   architecture: Haswell
    num_threads: 20
```

COMMENT:
Actually I think that you are using a multi-output `y`:

```python
import numpy as np
from sklearn.metrics import mean_squared_error

rng = np.random.default_rng(0)
y_true = rng.normal(size=(10, 2))
y_pred = rng.normal(size=(10, 2))
# make the first output in a different range
y_true[:, 0] *= 100
y_pred[:, 0] *= 100

mse = mean_squared_error(y_true, y_pred)
rmse = mean_squared_error(y_true, y_pred, squared=False)

print(mse)
print(rmse)
print(np.sqrt(mse))
```

```
In [1]: %run tmp.py
7609.0424975977185
62.18219863657098
87.22982573407859
```

The reason for the difference is that we apply `np.sqrt` on each individual output and then average the output. This is not equivalent to averaging and applying the square root (that is incorrect).

We don't have a bug, therefore. @tgnazmi98 if this is not the case, let me know I will reopen the issue.

Labels: Bug, Needs Triage