Question

Prove that 2-5 root 3 is irrational

Answer 1

Answer: let us assume that 2-5 root 3 is rational such that they are equal to  p/q where p and q are co prime

               2-5 root 3 =p/q

       -5 root 3 =p/q-2

         5 root 3 =2 -p/q

       5 root 3 =2 q- p/q

       root 3 =2 q -p/5 q [ rational/rational]=rational so rhs is rational

     but we know root 3 is irrational

  hence our assumption is wrong that 2-5root 3 is rational so 2-5 root 3 is irrational

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