Question

Show that root 7 minus root 3 is an irrational number

Answer 1

Let us assume that root 7 - 3 is rational.

=>root7  - 3=a/b

root 7= a/b -3

a/b and -3 are rational numbers but root 7 is irrational.

It is a contradiction

Therefore , our assumption that root 7 - 3 is rational is false. 

Therefore, root 7 - 3 is irrational

Hence proved