Question

Show that 4+√2 is irrational number

Answer 1

let us assume that 4+√2 is rational

we know that every rational number can be expressed as p/q

i.e. 4+√2=p/q

transposing 4 to the other side

√2=p/q- 4

√2=p-4q/q

since p and q are integers p-4q/q is also rational and so √2 is also an integer

this contradicts the fact that √2 is irrational

so 4+√2 is also irrational

this it is proved that 4+√2 is irrational

proved,,,