Question

prove that√5-√3is not rational with steps plzzzz

Answer 1

hey

let root5 - root 3 is a rational number.
and equals to k

root5 - root3 = k

by squaring both sides..

(root5-root3)^2 = k^2.

8 + 2root15 = k^2.

root15 = (k^2- 8)/2

so RHS is rational
but
LHS is irrational.

(contradiction)

so proved.....