Question

show that 2 minus root 3 is irrational numbers

Answer 1

let us assume that 2-√3 is rational.
so it can be written of form a/b (b≠0) where both a and b are co-primes
so, 2-√3 = a/b
⇒ √3 = 2- a/b
here a, b and 2 are integers. so 2- a/b is rational.
so √3 is also rational.
but this contradicts the fact that √3 is irrational (as we know it is irrational).
this contradiction has rise due to our wrong assumption of 2-√3 as rational.
 hence, it is irrational.

Answer 2

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