Question

Prove that 5-√3 is irrational....

Answer 1

Refer to the attachment !

Answer 2

Answer:

let us assume that 5-√3 is rational no.

so, 5-√3= p/q, where p and q are co prime nos.

-√3 = p/q-5=p-5q/q

√3 =-(p-5q/q)

this shows that √3 is rational no.

but this contradicts the fact that √3 is a rational no.

hence our assumptions is wrong.

thus, 5-√3 is irrational

HENCE PROVED