Question

prove that √7 is an IRR No ?​

Answer 1

Answer:

Hope it will helps you :)

Step-by-step explanation:Let us assume that  

7

​  

 is rational. Then, there exist co-prime positive integers a and b such that

7

​  

=  

b

a

​  

 

⟹a=b  

7

​  

 

Squaring on both sides, we get

a  

2

=7b  

2

 

Therefore, a  

2

 is divisible by 7 and hence, a is also divisible by7

so, we can write a=7p, for some integer p.

Substituting for a, we get 49p  

2

=7b  

2

⟹b  

2

=7p  

2

.

This means, b  

2

 is also divisible by 7 and so, b is also divisible by 7.

Therefore, a and b have at least one common factor, i.e., 7.

But, this contradicts the fact that a and b are co-prime.

Thus, our supposition is wrong.

Hence,  

7

​  

 is irrational.

Answer 2

Answer:

An answer by techbros614.

Step-by-step explanation:

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