Question

Does square root of 162 = square root of 81 and square root of 81 added

Answer 1

No because you would have to do the square root of two times the square root of 81 if you want to get the square root using 81

The square root in a non linear function.

Answer 2

No.
.. √162 = (√2)*(√81)
.. √81 +√81 = 2√81 = √324

Square root is a non-linear function. sqrt(a +b) ≠ sqrt(a) +sqrt(b)