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If we assume that the sqare root of 5 is a rational number, then we can write it as a/b in its simplest form, where a and b have no common factors.

Therefore 5 = a2/b2

Therefore 5b2 = a2

Therefore a2 is divisible by 5, because b2 is an integer

Therefore a is divisible by 5, because 5 is a Prime number.

Therefore 5 = 5c/b, where c is an integer

Therefore 1 = c/b

Therefore c = b

Therefore sqrt 5 = 5c/c = 5, which is impossible.

So sqrt5 cannot be expressed in the form a/b, and is irrational.

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15y ago

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