Question

Find the domain of the function g (X) =square root of 2_square root of p solve the problem

Answer 1

not sure what you mean. Since g(x) really ought to include an x (and no p),
the domain of √x is x≥0
I guess you meant

g(x) = √(2-√x)
with domain (2-√x) ≥ 0 or √x ≤ 2 or x ≤ 4
or
g(x) = √2 - √x
with domain x ≥ 0

If you meant something else, try using real math notation instead of ambiguous words

It's not my job to figure out what you mean.
It's your job to say it so clearly you cannot be misunderstood.

Answer 2

If your question means:

√ ( 2 - √ p )

then

p must be ≥ 0

because for p < 0 , √p is complex conjugate

p must be ≤ 4

because for p > 4 , 2 - √ p is negative

In this case √ ( 2 - √ p ) is also complex conjugate

So domain is:

0 ≤ p ≤ 4

Or in interval notation:

[ 0 , 4 ]