Question

Prove that 6-5√7 is an irrational number

Answer 1

first we will prove that root 7 is irrational number

let root 7 is irrational number

so we can write it in the form of p by q where Q is not equal to zero

root 7 equals to P by q let P and Q as coprime number

so, 7p=q

it contradicts because we have let that p and q are coprime number but it has another factor except one so are assumption on is wrong .

root 7 is irrational

if use any operation with any rational number answer will always be irrational so 6 minus 5 root 7 is also a irrational hence proved