Question

prove that √5,√6are irrational

​

Answer 1

Answer:

Step-by-step explanation:

Hey mate here is your answer.

It can be expressed in the form p/q where p,q are co-prime integers. Hence, p,q have a common factor 5. ... Therefore, p/q is not a rational number. This proves that √5 is an irrational number.

The following proof is a proof by contradiction.

Let us assume that  

6

​  

 is rational number.  

Then it can be represented as fraction of two integers.  

Let the lowest terms representation be:  

6

​  

=  

b

a

​  

 where b  



​  

=0

Note that this representation is in lowest terms and hence, a and b have no common factors

a  

2

=6b  

2

 

From above a  

2

 is even. If a  

2

 is even, then a should also be even.

⟹a=2c

4c  

2

=6b  

2

 

2c  

2

=3b  

2

 

From above 3b  

2

 is even. If 3b  

2

 is even, then b  

2

 should also be even and again b is even.

But a and b were in lowest form and both cannot be even. Hence, assumption was wrong and hence,  

6

​  

 is an irrational number.

Answer 2

Answer:

√5 and√6 is irrational because it cannot be expressed in p/q form