Question

Prove that are irrational by contradiction method. 5+3√2

Answer 1

Solution.

Let 5+3root2 is a rational no. is equal to r where r is a rational no.

So

$5 + 3\sqrt{2} = r$

$3 \sqrt{2} = r - 5 \\ \\ \sqrt{2 } = \frac{r - 5}{3}$

Here LHS is an irrational no. and RHS is a rational no.

So, our assumption was wrong.

5 + 3root2 is not a rational no.

Therefore 5 + 3root 2 is an irrational no.

Hence Proved .