Question

Prove that 1/ under root 11 is an irrational number

Answer 1

Let us assume √11 is rational number.

√11 = a/b (. Where a&b are co - prime number.)

b = a√11

b^2=11a^2. - (1)

b^2/11 =.a^2

So 11 is factor of a.

so let,

b/11 = k

b = 11k

b^2 = 121k^2

11b^2 = 121k^2

b^2=11k^2

So, 11 is factor of b also.

As, a&b have 11 as there common factor so they are not co-prime number.

So, our assumption is wrong.

√11 is irrational number.