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.
is √ (m^2 + n^2) an integer?
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- sanju09
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(1) m² + n² is an integer does not necessarily imply that √(m² + n²) is an integer; NOT sufficient.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.
(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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