Question

show that 2-root3 is an irrational number​

Answer 1

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Answer 2

Let us assume to the contrary that 2-√3 is rational. so,we can find coprimes a and b such that 2-√3=a/b where b≠0

so,√3=2-a/b

√3=2b-a/b

since 2,a and b are integers,2b-a/b is rational. so √3 is also rational. but this contradicts the fact that √3 is irrational. this contradiction has arisen because of our incorrect assumption that 2-√3 is rational. so,2-√3 is irrational