Question

prove that root 2 is an irrational number​

Answer 1

HEY MATE HERE IS YOUR ANSWER

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Answer 2

Answer:

The method of Contradiction

Step-by-step explanation:

Let root 2 be rational number

Then root 2=a/b. (where a and b are coprime numbers)

squaring both sides √2^2=(a/b)^2

Then we get 2 = a^2/b^2

It imples that 2b^2=a^2 .........(equation 1st)

So, 2 divides a^2

Then 2 Also divides a.......(theorem 1.3)

therefore 2c =a ( let c is constant)

putting this value in equation 1st

then we get

2b^2=a^2

2b^2=(2c)^2

2b^2= 2c^2

so 2 divides b^2

then 2 also divides b ......(by 1.3 theorem)

therefore a and b have atleast 2 as a common factor

So, This Contradicts the fact that a and b have no common factor..

So, our contradiction is wrong and √2 is irrational number