Question

prove that root five is irrational​

Answer 1

To prove that √5 is irrational by contradiction method.

Let us consider √5 to be rational 

Then, It can be expressed as √5 = a/b ( where a, b are integers and co-primes)

√5 = a/b

5= a²/b² 

5b² = a²

5 divides a²

By the Fundamental theorem of Arithmetic

so, 5 divides a .

a = 5k (for some integer) 

a² = 25k² 

5b² = 25k² 

b² = 5k² 

5 divides b²

5 divides b. 

Now 5 divides both a & b this contradicts the fact that they are co primes. This is a contradiction

This contradiction has arises due to our faulty assumption that √5 is rational. Hence, √5 is irrational. 

Answer 2

Answer:

Step-by-step explanation: