Question

prove that root3 + root5 is a irrational​

Answer 1

Answer:

root 3 + root 5 is an irrational number

Answer 2

Answer:

It is irrational

step-by-step explanation:

Let us assume √3+√5 are rational numbers

Let √3+√5=p/q, a,b are co-primes

√3=p/q-√5

Square on both sides,

(√3)^2= (p/q-√5)^2

3=p^2/q^2+(√5-2(p/q)(√5))

√5 x 2p/q=p^2/q^2+5-3

√5 (p^2+2q^2/q^2)x q/2p

√5 is rational but the RHS is irrational

Hence, the √3+√5 is irrational.