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is √ (m^2 + n^2) an integer?

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by sanju09 » Sat Oct 08, 2011 3:32 am
If n is an integer, is √ (m^2 + n^2) an integer?

(1) m^2 + n^2 is an integer.

(2) m^2 - 3 n^2 = 0.
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by Anurag@Gurome » Sat Oct 08, 2011 3:49 am
sanju09 wrote:If n is an integer, is √(m^2 + n^2) an integer?

(1) m^2 + n^2 is an integer.

(2) m^2 - 3 n^2 = 0.
(1) m² + n² is an integer does not necessarily imply that √(m² + n²) is an integer; NOT sufficient.

(2) m² - 3n² = 0 implies m² = 3n² (m - n√3)(m + n√3) = 0
√(m² + n²) = √(3n² + n²) = √(4n²) = 2n, -2n
Since n is an integer, so √(m² + n²) will also be an integer; SUFFICIENT.

The correct answer is B.
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