Question

Prove that 7+4√2 is irrational

Answer 1

let us assume that 7 + 4 root 2 is a irrational number

7+4√2=p/q,. pq€z

4√2=p-7q/q

√2=p-7q/4q

wkt p-7q/4q is a rational no but

√2is not s rational number

it is contradictory to our assumption and our assumption is wrong

terefore it is a irrational number

Answer 2

Let's assume that it's a rational and it's equal to a/b which is another rational

7+4root2 =a/b

4 root2 =a/b - 7

root2 = a - 7b /7 /4

root2 = a - 7b/ 28

since the lhs is irrational and rhs is a rational.

therefore 7+4root 2 is also irrational