Question

Show that 5+√2 is not a rational number

Answer 1

Let 5+√2 be a rational number,
A rational number can be written in the form of p/q.
5+√2=p/q
√2=p/q-5
√2=(p-5q)/q
Therefore,p,q are integers then (p-5q)/q is a rational number.
Then √2 is also a rational number.
But this contradicts the fact that √2 is an irrational number.
So,our supposition is false.

Thus,5+√2 is an irrational number
Hence proved.

Hope it helps

Answer 2

let 5+√2 is rational no.
so 5+√2 = p/q ( where p and q are co prime number)
√2=p/q-5
√2= p-5q/q
that, √2 is irrational numbers
but, p-5q/q is rational number
so, 5+√2 is irrational numbers

Hope you get your ans..