Question

show that root 2is irrational

Answer 1

Heya buddy!!
Pleasure to help you with this question :-))

Here is the proof for that root 2 ir irrational number.
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Let us assume to contrary that root 2 irrational.
So we can find integers r and s (not = 0) such that
root 2=r/s
Suppose r and s has common factor other than 1.Then divide both r and s by the common factor to get root 2 =a/b where a and b are co prime.
So a=b* root 2
Squaring both sides--> a^2=2b^2
thus 2 divides a^2.
Then by theorem which states "Let p be a prime number.lf p divedes a^2 ,then p divides a where a is a positive intiger."
So we can write a=2c for some integer c
Substituting for a ,we get 2b^2=4c
i.e. b^2=2c^2
This means that 2 divides b^2
Then by theorem stated above ,2 divides b.
Therefore a and b have atleast 2 as common factor.But this contradicts the fact that a and b are coprime (have no factors other than 1 )
So our assumption is wrong.
Therefore ,root 2 is irrational
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Hope it helps

Answer 2

hii frnd .. chk it out the solution the pic ..