Question

Given that √2 is irrational, prove that (5+3√2) is an irrational number?

Answer 1

let 5+3√2 be rational such that 5+3√2= a, where 'a' is a rational number.

Now,
5+3√2 =a

3√2= a-5 (subtraction of a rational no. from a rational no. is rational)

√2= a-5/3. (division of a rational no. by a rational no. is rational)

But this is not possible as we know that √2 is irrational.
Thus, 5+3√2 is irrational.