Question

If root 2 is not a rational number then prove that 2 + root 2 is not a rational number

Answer 1

Answer:

let assume that 2+√2 is a rational number

then, there exist co-prime number a and b (b not equal to 0)

$2 + \sqrt{2} = \frac{a}{b}$

$\sqrt{2} = \frac{a}{b} - 2$

$\sqrt{2} = \frac{a - 2b}{b}$

since a and b are integers, so

$\frac{a - 2b}{b}$

is rational.

thus, √2 is also rational.

but, this contradicts the fact that √2 is irrational. So, our assumption is incorrect.

hence, 2+√2 is not a rational number i.e. irrational number.

prooved✔️✔️✔️

Answer 2

Hope it helps u the answer is given in the picture