Question

Prove that (3+2√5)^2 is irrational

Answer 1

Step-by-step explanation:

(a+b)²=a²+b²+2ab

(3+2√5)²=3²+(2√5)²+2(3(2√5)

=9+20+12√5=29+12√5

let it b equal to p/q

29+12√5=p/q

12√5=p/q-29

12√5=p-29q/q

√5=p-29q/12q

p-29q/12q is rational.

But, √5 is irrational

so(3+2√5)² is irrational.

Answer 2

Answer:

answer attached in photo