Question

Prove that ✓5 is irrational
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

let us assume that $\sqrt{5}$ is rational

thus, we can write it as $\sqrt{5}$ =a/b,where a and b are coprimes and b is not = 0

so , $b\sqrt{5}$ = a

on squaring them we get

$5b^{2} =a^{2}$

there fore a(square) is divisible by 5

so,we can write a=5c

on substituting a we get,

$5b^{2} =10c^{2}$

that is $b^{2} =5c^{2}$

that means b is also divisible by 5

therefore a and b have atleast 5 as cmmon factor

but this contradicts the fact that a and b are coprimes

and this has arisen due to our incorrect assumption that $\sqrt{5}$ is irrational

. So $\sqrt{5}$  is irrational