Question

Prove that root5 - root3 is not a rational no.

Answer 1

This can be answered by contradictory method

Assume √5-√3as rational number where (p,a are X and p,a are co primes about equal to 0)

√5-√3=p/q

Sons

(√5-√3)whole square=(p/q) whole square

5+3-2(√15)=psquare/square

8-2√15= """"

-2√15 =p^2/q^2-8

-2√15=p^2-8q^2/q^2

2√15=8q^2-p^2/q^2

As we know that 2√15 is irrational &the rhs is rational

Hence proven that it is not rational no