Question

Prove that √3+√5 is an irrational number​

Answer 1

let √3+√5 be any rational no. X

x=√3+√5

squaring both the side of the equation

x^2=(√3)^2+(√5)^2+2√15

x^2=8+2√15

x^2-8=2√15

x^2-8/2=√15

as X is a rational so x^2 should also be an rational and 8&2 are rational , so √15 should also be an rational

but √15 is an irrational

this proves that √3+√5 is an irrational no.