a)let a be a positive integer.If square root of a is rational, prove that square root of a is an integer.

b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.

PLease help me this one.

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- Jan 27th 2010, 02:22 PMDeepuabstract algebra proof
a)let a be a positive integer.If square root of a is rational, prove that square root of a is an integer.

b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.

PLease help me this one. - Jan 27th 2010, 03:47 PMhatsoff
This is proved here:

Quadratic irrational - Wikipedia, the free encyclopedia

Quote:

b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.