Question

Prove that 2 root 11 is irrational

Answer 1

Step-by-step explanation:

1. Let us assume 2√11 is rational.
2. therefore, it can be written as p/q, where q=/=0
3. so, 2√11 = p/q
4. (taking 2 on other side), √11 = p/2q
5. LHS is irrational, and RHS is rational. This contradiction has occured due to our incorrect assumption that 2√11 is rational.
6. therefore, 2√11 is irrational.

Answer 2

hey mate...

here is your answer...

Also, it implies that a^2 is a multiple of 11. Since 11 is prime, a will also be a multiple of 11. Hence our initial assumption doesn't hold true and sqrt(11) is irrational! The same proof can be extended to prove that the square roots of all prime numbers are irrational!

hope it helps...