Question

Plz explain step by step

Answer 1

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Answer 2

Answer:

let us assume that root3 is rational

so now root3 can be written in p/q form where p and q (q not equal to 0) are coprime( no common factor other than 1)

hence

   p = root 3q

now squaring both sides

( root 3q)square= p square

or,  3q square= p square______(1)

p square/3 =q square

therefore 3 is a factor of p

p=3c( where c is a constant)

substituting p=3c in equation 1,

( 3c )square= 3q square

or, 9c square= 3q square

or, 3c square= q square

or, c square=  q square/3

therefore 3 is also a factor of q. but this is a contradiction.

therfore root3 is an irrational number.( proved )

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