Magnitude of vector: Error in lecture video?

In “Projection of one vector onto another”, the formula for magnitude used is Screenshot (228)
but actual formula is
Annotation 2020-06-03 124833
Then in the video, it is wrong or there is any intuition behind this?

Yes, the given calculation is incorrect.
Please mark it on your side.

It should have been:
||y||^{2} = 2^2 + 2^2 + 1^2 = 9 (without the square root)
Or ||y||^{2} = (\sqrt{2^2 + 2^2 + 1^2})^2 = 9

Formula is correct.

. Multiply (11/3) with unit vector of y.