Question

Prove that 5 +√ 2 is irrational number

Answer 1

Step-by-step explanation:

Let 5+√2 be a rational no.

Answer 2

let if possible 5+/2 be a rational number

then there exist two integers a & b where b not equal to 0 and a & b are prime numbers

such that a/b = 5+/2

i.e, a/b-5= /2

a-5b/b=/2

we know that a-5b/b is a rational number

which implies /2 is a rational number but this contradict the fact that /2 is a rational number

therefore our supposition is wrong

Hence 5+/2 is irrational number