Bunuel wrote:

If m and n are positive integers, is \((\sqrt{m})^n\) an integer?

(1) \(\sqrt{m}\) is an integer.

(2) \(\sqrt{n}\) is an integer.

Hi,

Difficulty level: 600

We have to find whether \((\sqrt{m})^n\) is an integer,

or \(m^{\frac n2}\) is an integer.

Given, m & n are integers,

Using (1),

\(\sqrt{m}\) is an integer

then, \((integer)^{(integer)}\) is Integer. Sufficient.

Using (2),

\(\sqrt{n}\) is an integer, or n is an integer.

lets say, m=3, n=9,

\((\sqrt{m})^n\)=\((\sqrt{3})^9\) which is not an integer. Insufficient.

Thus, Answer is (A)

Regards,

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