If m And n Are Positive Integers, Is Root(m)^n An Integer? GMAT Data Sufficiency

Question: If m and n are positive integers, is \((\sqrt m)^n\) an integer?
(1) √m is an integer.
(2) √n is an integer.

       A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
       B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
       C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
       D) EACH statement ALONE is sufficient.
       E) Statements (1) and (2) TOGETHER are not sufficient.

Approach Solution 1

Approach Solution 2

Approach Solution 3

“If m and n are positive integers, is root(m)^n an integer?" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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