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Prove that 5 is irrational.

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Prove that 5 is irrational.
  • 1 answers

Himanshi Thakur 2 months ago

Let √5 be a rational number. then it must be in form of pq where, q≠0 ( p and q are co-prime) √5=pq √5×q=p Suaring on both sides, 5q2=p2 --------------(1) p2 is divisible by 5. So, p is divisible by 5. p=5c Suaring on both sides, p2=25c2 --------------(2) Put p2 in eqn.(1) 5q2=25(c)2 q2=5c2 So, q is divisible by 5. . Thus p and q have a common factor of 5. So, there is a contradiction as per our assumption. We have assumed p and q are co-prime but here they a common factor of 5. The above statement contradicts our assumption. Therefore, √5 is an irrational number.
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