Question

Prove that√ 5 - √3 is irrational.​

Answer 1

let us suppose that √5-√3 is rational number

√5-√3 = p/q ( where p is not equal to q and both are co

prime numbers )

BY SQUARING BOTH SIDE

5+3+2√15 = p^2/q^2

2√15 = p^2-8q^2 /q^2

√15 = p^2-8q^2 /2q^2

√15 is irrational

p^2-8q^2 /2q^2 is rational

WE KNOW THAT IRRATIONAL IS NEVER EQUAL TO RATIONAL ,

SO, IT IS A CONTRADICTION

THEREFORE , OUR SUPPOSITION IS WRONG

HENCE , √5-√3 IS IRRATIONAL