Question

prove that 1/√11 is an irrational number​

Answer 1

Assume to reach our contradiction that 1/√11 is rational.

So that 1/√11 can be written as p/q, where p, q are coprime integers and q ≠ 0.

Thus,

$\displaystyle \frac{p}{q}=\frac{1}{\sqrt{11}}$

Taking the reciprocals...

$\displaystyle \frac{1}{\frac{p}{q}}=\frac{1}{\frac{1}{\sqrt{11}}} \\ \\ \\ \\ \Rightarrow \ \frac{q}{p}=\sqrt{11}$

Here it creates a contradiction that, the LHS p/q is rational while the RHS √11 is irrational. Here it seems that √11 can be written in fractional form.

Hence our earlier assumption is contradicted and reached the conclusion that √11 is irrational.

Answer 2

Answer:

hence prove that 1/√11 is an irrational