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If P is a prime number , then prove that square root of P is irrational
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If P is a prime number , then prove that square root of P is irrationa...
By way of contradiction, assume p–√ is rational. Then there exist a,b∈Z with b≠0 such that p–√=ab. Without loss of generality, we may assume gcd(a,b)=1. Then p=a2b2. Thus p|a2 which implies p|a, i.e., ∃k∈Z such that pk=a. We now have pb2=(πk)2=p(pk2), so pb2=a2. Since p≠0, b2=pk2, which means p|b. Thus p is a common factor of a and b. This is a contradiction as a and b are relatively prime.
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If P is a prime number , then prove that square root of P is irrational
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If P is a prime number , then prove that square root of P is irrational for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If P is a prime number , then prove that square root of P is irrational covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P is a prime number , then prove that square root of P is irrational.
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