Question

prove that 5+root2 is irrational number

Answer 1

Answer:

Let's assume that 5+ 2 is a rational no.

So it can be expressed in the form of a/b form where a and b are integers.

So: 5 root2=a/b

=2=a-5b/b

Since a and b are integers so a-5b/b is rational no. which implies that 5+root2 is also rational no.

But it contradicts the fact that root 2 is irrational no. Therefore our assumption is wrong, 5+root2 is irrational no.