Question

prove that 2-8√3 is an irrational number​

Answer 1

Answer:

yes ,it is an irrational no.

Step-by-step explanation:

let 2-8√3 is rational no.

2-8√3=p/q( where p and q are coprimes and q is not equal to 0)

-8√3=p/q-2

-8√3=p-2q/q

√3=p-2q/-8

√3=-(-p+2q/8)

here rhs is rational no

therefore √3 is rational no

but this contradict the fact that √3 is irrational no

and this contradiction is arisen due to our wrong assumption that 2-8√3 is rational no

therefore 2-8√3 is an irrational no