Question

prove that root 11 - root 3 is irrational

Answer 1

Answer:

suppose root 11-root 3 is rational

let root 11-root 3=p/q(where p, q are co- primes)

squaring on both sides

(root 11-root3)2=(p/q)2

11-3 11root9=p2/q2

8- 11root 9=p2/q2

11 root 9=p2/q2-8

11 root 9=p2-8q/q2

root 9=p2-82/11q2

I.e irrational number =rational number

which is a contradiction.

therefore, our assumption is false.

Hence, root 11-root 3

I hope it helps you..