Is the positive square root of x an integer? (1) x = n^3 and n is a pe

Is the positive square root of x an integer?
Two properties of Perfect Square which will be handy in solving the question
- Perfect Square is true for integers only
- The number of distinct factors of a Perfect Square is Always Odd

(1) \(x=n^3\) and n is a perfect square.
Since n is a perfect square, say n = \(a^2\), where a is an integer
then, x = \(n^3\) = \((a^2)^3\) = \(a^6\)
and \(sqrt x = sqrt(a^6) = a^3 \)-> which is an integer. Hence st1 is Sufficient.

(2) x has exactly seven factors.
since x has odd number of distinct factors (7) therefore, x is a Perfect Square
\(x = b^2\), where b is an integer
and \(sqrt x = sqrt(b^2) = b\) -> which is an integer. Hence st2 is Sufficient.
Answer: D