Question

if √2 is given as an irrational number, then prove that ( 7-2√2 ) is an irrational number​

Answer 1

Answer:

let √2 be a rational number

hence, 7-2√2 can be written in the form of a/b

7-2√2= a/b

-2√2=a/b -7

-2√2= a-7b/b

√2= a-7b/2b

This shows that (a-7b)/2b is rational. But we know that √2 is an irrational number.

So, it contradicts our assumption.

Therefore, 7-2√2 is an irrational number.

Hence, Proved.