Question

prove that 8-2 root 3 is irrational number​

Answer 1

Let 8-2√3 be rational no.

8-2√3 = p /q ( where p and q are co prime and q ≠0)

√3 = -p/2q +8/2

In LHS side there's Irrational no. and in RHS there is a rational no. This is not possible. This contradiction arise due to our wrong assumption. Thus our assumption is wrong.

8-2√3 is Irrational no.

Hence proved

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