Question

prove that 4/√3 is an irrational number​

Answer 1

Answer:

Step-by-step explanation:

Let us assume the contrary, that 4−  

3

​  

 is rational.

That is, we can find co-prime a and b (b



=0) such that 4−  

3

​  

=  

b

a

​  

.  

Therefore 4−  

b

a

​  

=  

3

​  

.

Rearranging this equation, we get  

3

​  

=4−  

b

a

​  

 

=  

b

4b−a

​  

 

Since a and b are integers, we get  

b

4b−a

​  

 is rational, and so  

3

​  

 is rational.

But this contradicts the fact that  

3

​  

 is irrational,

This contradicts the fact that  

3

​  

 is irrational.