Question

 Prove that √3 -√2 is irrational number. Is (√3 + √2)(√3 + √2) is Rational or Irrational number?​

Answer 1

√3-√2 as irrational

let us assume √3-√2 is rational and and they are in the form of p/q

√3-√2=p/q

√3=p/q-√2

as we know that √3 is irrational then p/q-√2 is also irrational

LHS = RHS

and like wise √3-√2 is also irrational

(√3+√2)(√3+√2)

== (√3+√2)^2

=√3^2 + √2^2+2(√2)(√3)

=3+2+2√6

=5+2√6

it is an irrational number so (√3+√2 )^2 is also irrational