Question

Prove that 5-2√2 is an irrational

Answer 1

5-2√2

let 5-2√2 be a rational no.

5-2√2 = a/b

-2√2 = a/b-5

-2√2 = a-5b/b

-√2 = a-5b/2b

5b-a/2b=√2

√2 is an irrational no. so 5b-a/2b should also be an irrational no.

therefore , our assumption is wrong .

5-2√2 is an irrational no.