Question

Prove that 2-v3 is irrational, given that v3 is irrational. class 10 ​

Answer 1

Let 2-√3 be rational

so, 2-√3 can be written as p/q where p/q are coprime integers.

2-√3 = p/q

-√3=p+2q/q ———(1)

Now it is given that √3 is Irrational so in eq. (1) LHS is Irrational But RHS is Rational. Therefore This Leads to A contradiction And Our Assumption Must be Wrong.

therefore 2-√3 = Q' = Irrational

Hope it Helps

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