Question

Prove that6+√2 is irrational

Answer 1

Please Check Attachment for Solution,

tq.

Answer 2

Answer:

Step-by-step explanation:

Let us assume 6+√2 is rational. Then it can be expressed in the form

p/q

​

, where p and q are co-prime

Then, 6+√2 = q

p

​

√2 = p −6

q

​

√2 = p−6

​ q

-----(p,q,−6 are integers)

√2 = p−6

q

​

is rational

But, 2

​

is irrational.

This contradiction is due to our incorrect assumption that 6+

2

​

is rational

Hence, 6+√2

​

is irrational