Question

show that 5 + 3root2 is an irrational number

Answer 1

Let 5+3√2 be rational.
5 is also rational
The difference of two rational no. is rational.
Therefore, 5+3√2-5
= 3√2 which must be rational.
1/3 is also rational.
The product of two rational no. is rational
Therefore,
1/3(3√2)=√2 is rational.
This contradicts the real fact that √2 irrational.
Therefore, our assumption was wrong
5+3√2 is irrational.