My take would be E
Using both equations it can be seen that z^2 is integer and question states that z is + integer,but these two are not sufficient.

for eg let z=2,z^1/2 not an integer
and if z = 4,z^1/2 = 2 is an integer

i am not sure what u asking !!
but the answer i feel is E
the final step of urs that Z^2 =int is not sufficient to decide if z^1/2 is an int
logic is simple Z^2 =1 -----> z^1/2 is an int
and Z^2 = 9 ---->z^1/2 is not an int

Deepthi Subbu wrote:If z is a positive integer, is √z an integer?

(1) √(xz) is an integer.
(2) x = z³

Question rephrased: If z is an integer, is z a perfect square?

Both statements are satisfied if z=1 and x=1³=1, in which case z is a perfect square.
Both statements are satisfied if z=2 and x=2³=8, in which case z is not a perfect square.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.

Algebraically:
Substituting x=z³ into statement statement 1, we get:
√(z³z) = integer
√(z^4) = integer
z² = integer.
ANY POSITIVE INTEGER will satisfy this equation:
1² = integer.
2² = integer.
3² = integer.
And so on.
Thus, it's possible that z is a perfect square or that z is not a perfect square.

Please note the following:
When the statements are combined, non-integer values such as z=√2 satisfy the condition that z² = integer.
But these non-integer values do NOT satisfy the constraint given in the question stem: z is a positive integer.
Because of this constraint in the question stem, ONLY POSITIVE INTEGER VALUES for z can be considered when we evaluate the two statements.