Question

Prove that root 2 + root 7 is an irrational number

Answer 1

Answer:

using indirect proof

let us assume that it is not a irrational.number

this means it is a rational number

means it can be written in the form of p by q

therefore, 2+root7=p by q

root7= p by q- root 7

here right hand side is a rational number but left hand side is irrational

this is contradictory because our assumption is wrong

so by correcting our assumption, we get

this is a.rational.number

hence proved