Question

show that √3+√5 is an
irration​3+​

Answer 1

let us assume that root 3 + root 5 is rational and its core Prime are p and q .

root 3 +root 5=p/q

root 5=p/q-root 3

(root 5)^2=(p/q-root3)^2 (squaring both side)

5=P^2/q^2-2p root 3/q+3

2p root3/q=p^2/q^2+3-5

2p root3/q=p^2/q^2-2q^2

root3=p^2/q^2-2q^2×q/2p

root 3= p^2 -2q^2/2pq

since root 3 is an irrational number,but p^2-2q^2/2pq is an rational number ,which is contradicts, so,our assumption is wrong ,hence (root 3+root 5) is an irrational number.

Hope it will help you...