Question

Prove that 3 + 2 root 5 whole square is irrational

Answer 1

Answer:

(3+2root 5)^2 =(3)^2 +(2root5) ^2 +2.3.2root5  

=9+20+12root5

=29+root720(because root720 is irrational no. so whole no. is irrational)  

THANKS

Step-by-step explanation:

Answer 2

Answer:

To Prove : (3 + 2√5)² is irrational No.

First we simplify using identity, (a+b)² = a² + 2ab + b²

(3 + 2√5)² = 3² + (2√5)² + 2×3×2√5

                = 9 + 4×5 + 12√5

                = 29 + 12√5

we use the result that √5 is an irrational no.

we know that product of rational and irrational no is and irrational no.

⇒ 12 × √5 = 12√5 is an irrational no.

Now, Addition of a rational no with irrational given an irrational no.

⇒ 29 + 12√5 is an irrational no.

since, 29 + 12√5 = (3 + 2√5)²

⇒ (3 + 2√5)² is an irrational .

Hence Proved