Question

prove that 3 + 5 root 2 is an irrational number​

Answer 1

let 3+5√2 be rational number.

3+5√2 =p/q (where p and q are integers and q is not equal to zero)

5√2 = p/q-3

As we know that the difference of rational number is rational but here the difference is irrational, because √2 is irrational so 5√2 Is also irrational.

So, our assumption is wrong,

3+5√2 is an irrational number.

Hence, we proved that 3+5√2 is an irrational number not an rational number.

HEre is Your AnSWER.