Question

prove that 5-3/root2

Answer 1

Answer:

Given that    

2

​  

  is irrational.

We know that the theorem "The product of any irrational number with a rational number is irrational".

So, since we know  3  is a rational number,  3  

2

​  

  is irrational.  

(3=  

1

3

​  

;1



=0)

Now we know that  3  

2

​  

  is irrational.

Theorem:  The sum of a rational number with an irrational number is irrational.

So, since we know  5  is a rational number,  5+3  

2

​  

  is irrational.  

(5=  

1

5

​  

;1



=0)  

Thus we proved that  5+3  

2

​  

  is an irrational number.