Question

given that root 2 is irrational proof that graphics 5 + 3 root 2 is an irrational number ​

Answer 1

this may help you both are irraction according to contradiction

Answer 2

Given - √2 is a irrational no.

Let us assume contradict that 5 + 3√2 is a rational number.

5 + 3√2 = a / b {where a and b are co-

prime integers}

3√2 = a / b - 5

√2 = a / b - 5/3 -----------1

So , from equation 1

We observe that a / b - 5/3 is a rational number whereas we already know that √2 is a irrational number. So, they cannot be equal .So, our assumption is wrong 5 + 3√2 is a irrational number-- ----------------------Hence Proved --------------------