Question

Prove that 2 +2√2 is irrational.​

Answer 1

Step-by-step explanation:

We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.

...

A proof that the square root of 2 is irrational.

2 = (2k)2/b2

b2 = 2k2

2

Answer 2

Answer:

$2 + 2 \sqrt{2} \: is \: irrational$

Step-by-step explanation:

Let 2 + 2√2 be r.

Then, 2+2√2 = r

2√2 = r - 2.

Here, LHS is irrational while RHS r - 2 is rational.

Therefore, LHS not equal to RHS...

Hence, it contradicts our assumption that

$2 + 2 \sqrt{2}$

is rational. Hence, it is irrational number....