Question

2.Prove that V3 + V5 is irrational.​

Answer 1

Answer:

let as assume root 3 is rational no.

Answer 2

let us assume root 3 and root 5 are rational numbers so there. must exist two integers p/q

where q is not equal to zero. divide p/q if possible then we get a/b

r3+r5=a/b (r =root)

r3 =a/b -r5

r3=a/b -r5 /1. eq 1

squaring Both sides of eq 1

r3 square = a/d -r5 whole square

after calculating we will get

r3=a square + b square / 2ab

since a ,b are integers a square+b square /2ab is rational and so r3 irrational

this contradicts the fact that r3 is irrational

hence R2 +r3 is irrational.