InterviewSolution
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InterviewSolution
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11. If p is a prime number, then prove that p is irrational. |
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Answer» Let √p be a rational number.also a and b is rational.then,√p = a/bon squaring both sides,we get,(√p)²= a²/b²→p = a²/b²→b² = a²/p [p divides a² so,p divides a]Let a= pr for some integer r→b² = (pr)²/p→b² = p²r²/p→b² = pr²→r² = b²/p [p divides b² so, p divides b]Thus p is a common factor of a and b.But this is a contradiction, since a and b have no common factor.This contradiction arises by assuming √p a rational number.Hence,√p is irrational. |
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