Question

show that 7-root5is irrational give that root 5 is irrational

Answer 1

if root 5 is irrational...then 7- root 5 will also be irrational as we cannot equate a rational no. with an irrational no.

Answer 2

let 7√5 be rational

7√5=p÷q(p÷q is rational)

√5=(p÷q)÷7

here √5 is irrational but it is equal to a rational number this contradicts that 7√5 is a irrational number.