Question

16) Prove that root3 - root5 is irrational.​

Answer 1

Answer:

They are irrational.

Step-by-step explanation:

let v3 is rational

v3=a/b(where a/b are co prime)

bv3=a(By squaring)

b^2X3=a^2

3c=a(if 3 divides a^2 ,3 will divide a)

9c^2=a^2(squaring)

9c^2=3b^2

3c^2=b^2(if 3 divides b^2 , 3 will divide b)

this means that a and b have at least 3 as a factor.

but this contradict the fact that a and b are co prime

this contadiction arises as we let v3 rational