Question

Prove that 5 - root 2 is a irrational number

Answer 1

Note that : Sum , Product and difference of two rational numbers is a rational number...

Let if possible suppose , 5 - root(2) is a rational number

As 5 - root(2) is a rational number

=> ( 5 - root(2) ) - 5 is a rational number

=> 5 - root(2) - 5 is a rational number

=> - root(2) is a rational number

=> ( - root ( 2 ) ) × ( - 1 ) is a rational number

=> root(2) is a rational number

But this is a constraction as root ( 2 ) is an irrational number.

Thus our assumption was wrong , Hence 5 - root ( 2 ) is an irrational number.