Question

if√2 is irrational, then prove that (5+3√2) is irrational ​

Answer 1

Given ,

5 + 3√2 is irrational number

Let , 5 + 3√2 is a rational number

Thus ,

5 + 3√2 = a/b

3√2 = a/b - 5

√2 = (a - 5b)/3b

Here , √2 is irrational number and (a - 5b)/3b is rational number

Since , Irrational ≠ rational

$\therefore$ Our assumptions is wrong

Therefore , 5 + 3√2 is irrational number