Question

prove that (3+2root5)^2 is irrartional

Answer 1

Step-by-step explanation:

To Prove :

(3 + 2√5)² is irrational,.

Proof :

Remember,

The identites and ideas used in this problem are :

(a + b)² = a² + 2ab + b² ,

√5 is irrational

and

Products & Sum of two Irrational numbers or a rational & an irrational is always irrational,.

(3 + 2√5)²

= (3)² + 2(3)(2√5) + (2√5)²

= 9 + 12√5 + 20

= 29 + 12√5

We know that,

29 is rational,

12√5 is irrational since, √5 is irrational

Hence,

29 + 12√5 is also irrational

⇒ (3 + 2√5)² is Irrational,.

Hence proved.