Q. 27

Prove that 2-√3 i

Answer :

Let 2 - √3 be a rational number

We can find co-primes a and b (b≠0) such that

2 - √3 = a/b

2 - a/b = √3

So we get, (2b - a)/b=√3

Since a and b are integers, (2b - a)/b is rational and so √3 should be rational. But √3 is an irrational number (Given).

Which contradicts our statement

Therefore 2 - √3 is irrational

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<span lang="EN-USRS Aggarwal - Mathematics